昨日の結果から、PDLPXについてCOPTサポートに問い合わせたところ、次の回答を得ました。
「私たちは独自の GPU 実装による PDHG とバリア法を開発しており、最新の Mittelmann ベンチマークによれば、LP に関してご指摘いただいたものを含む他の既知の GPU 実装を上回っています。これらの機能はすでに 8.0 リリースに含まれておりますので、ぜひお試しください。 」
とのことでした。日曜お昼に問い合わせしたら3分で返信がありました。
いうことで、真面目に比較評価してみた結果が次です。評価マシンは、同じですが、PDLPXの方は、WSL2でcmakeコンパイルしました。CUPDXコンパイルの注意点としては、CUDA TOOL-KIT 12.4 以上が必要です。これは、12.4から、cusparseSpMV_preprocess というAPIが追加されていてそれがCALLされている為です。
この結果を見ると、Instance24で明らかに、PDLPXの速度が速いことが分かります。この結果は、世界最高のCOPTのバリアソルバと比較しても2倍位速いです。
PDLPXの論文によれば、高精度程、その効果が大きいとの報告があり、実際にその傾向があることが上のデータから伺えます。今までのPDLPは、1e-4位を得意領域としていて、精度を上げると途端に遅くなる傾向にありました。それがPDLPXにおいては、1e-6程度でも実用域に入ってきたと感じます。また、本結果から、現在のCOPTがPDLPXを実装している訳ではないと推認されます。
現在の私が抱える課題の一つは、Instance24でLPソルバの速度が遅すぎることであり、PDLPXがその解決策になりうることを示しています。インスタンス毎に速度の優劣が変わってくるのは、常ではありますが、ことInstance24については、決定的な差です。現状COPTに期待が持てない以上、WarmStart等も評価して、実装を検討する必要がある、と結論します。instance24を解くにあたって最も時間がかかる処理は、Branch操作でありWarmStart性能がこの鍵です。バリアソルバは、この点において検討対象外です。
以下は、評価時のログになります。
COPT> set PDLPTol 1e-4
Setting parameter 'PDLPTol' to 0.0001
COPT> opt
Model fingerprint: 11cebb4f
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
14135 rows, 84693 columns and 11800327 non-zero elements
The presolved problem has:
13108 rows, 81336 columns and 11541827 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-04,5e-01]
Range of rhs coefficients: [1e-01,4e+00]
Range of bound coefficients: [2e-01,1e+02]
Range of cost coefficients: [9e-03,2e+04]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.11e+04 0.00e+00 3.73s
4000 +4.17407991e+04 +3.04897437e+04 +1.13e+04 2.98e+00 3.50e-01 6.08s
8000 +4.19070214e+04 +4.08247925e+04 +1.08e+03 1.13e+00 3.70e-02 8.24s
12000 +4.19414758e+04 +4.16358914e+04 +3.06e+02 4.70e-01 1.04e-02 10.39s
16000 +4.19482878e+04 +4.18529461e+04 +9.53e+01 1.90e-01 3.07e-03 12.56s
20000 +4.19509475e+04 +4.18808838e+04 +7.01e+01 1.31e-01 2.14e-03 14.72s
24000 +4.19503849e+04 +4.18968156e+04 +5.36e+01 8.06e-02 1.69e-03 16.88s
28000 +4.19513357e+04 +4.19022223e+04 +4.91e+01 6.54e-02 1.52e-03 19.04s
32000 +4.19500141e+04 +4.19077636e+04 +4.23e+01 5.78e-02 1.34e-03 21.22s
36000 +4.19503340e+04 +4.18930356e+04 +5.73e+01 4.79e-02 1.88e-03 23.39s
40000 +4.19512214e+04 +4.18980661e+04 +5.32e+01 4.64e-02 1.95e-03 25.55s
44000 +4.19517251e+04 +4.19044864e+04 +4.72e+01 4.24e-02 1.47e-03 27.73s
48000 +4.19519873e+04 +4.19109102e+04 +4.11e+01 3.67e-02 1.31e-03 29.92s
52000 +4.19507950e+04 +4.18687117e+04 +8.21e+01 4.05e-02 2.65e-03 32.12s
56000 +4.19510083e+04 +4.18951665e+04 +5.58e+01 3.67e-02 3.33e-01 34.31s
60000 +4.19508867e+04 +4.19031857e+04 +4.77e+01 2.64e-02 1.52e-03 36.49s
64000 +4.19502261e+04 +4.19103260e+04 +3.99e+01 2.44e-02 1.25e-03 38.67s
68000 +4.19505520e+04 +4.19165477e+04 +3.40e+01 2.03e-02 1.08e-03 40.88s
72000 +4.19510967e+04 +4.19211335e+04 +3.00e+01 2.19e-02 9.25e-04 43.09s
76000 +4.19509285e+04 +4.19249344e+04 +2.60e+01 1.64e-02 7.93e-04 45.30s
80000 +4.19510760e+04 +4.19055577e+04 +4.55e+01 2.56e-02 1.48e-03 47.51s
84000 +4.19506571e+04 +4.19217738e+04 +2.89e+01 1.92e-02 8.98e-04 49.72s
86760 +4.19508060e+04 +4.19424270e+04 +8.38e+00 2.89e-03 2.67e-04 51.26s
PDLP status: OPTIMAL
PDLP iterations: 86760
Primal objective: 4.19508060e+04
Dual objective: 4.19424270e+04
Primal infeasibility (abs/rel): 2.89e-03 / 2.61e-07
Dual infeasibility (abs/rel): 2.67e-04 / 3.07e-09
Duality gap (abs/rel): 8.38e+00 / 9.99e-05
Postsolving
Solving finished
Status: Optimal Objective: 4.1950806004e+04 Iterations: 86760(0) Time: 51.38s
COPT> set PDLPTol 1e-5
Setting parameter 'PDLPTol' to 1e-05
COPT> opt
Model fingerprint: 11cebb4f
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
14135 rows, 84693 columns and 11800327 non-zero elements
The presolved problem has:
13108 rows, 81336 columns and 11541827 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-04,5e-01]
Range of rhs coefficients: [1e-01,4e+00]
Range of bound coefficients: [2e-01,1e+02]
Range of cost coefficients: [9e-03,2e+04]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.11e+04 0.00e+00 3.76s
4000 +4.17407991e+04 +3.04897437e+04 +1.13e+04 2.98e+00 3.50e-01 6.28s
8000 +4.19070214e+04 +4.08247925e+04 +1.08e+03 1.13e+00 3.70e-02 8.46s
12000 +4.19414758e+04 +4.16358914e+04 +3.06e+02 4.70e-01 1.04e-02 10.64s
16000 +4.19482878e+04 +4.18529461e+04 +9.53e+01 1.90e-01 3.07e-03 12.82s
20000 +4.19509475e+04 +4.18808838e+04 +7.01e+01 1.31e-01 2.14e-03 15.00s
24000 +4.19503849e+04 +4.18968156e+04 +5.36e+01 8.06e-02 1.69e-03 17.18s
28000 +4.19513357e+04 +4.19022223e+04 +4.91e+01 6.54e-02 1.52e-03 19.36s
32000 +4.19500141e+04 +4.19077636e+04 +4.23e+01 5.78e-02 1.34e-03 21.54s
36000 +4.19503340e+04 +4.18930356e+04 +5.73e+01 4.79e-02 1.88e-03 23.73s
40000 +4.19512214e+04 +4.18980661e+04 +5.32e+01 4.64e-02 1.95e-03 25.93s
44000 +4.19517251e+04 +4.19044864e+04 +4.72e+01 4.24e-02 1.47e-03 28.13s
48000 +4.19519873e+04 +4.19109102e+04 +4.11e+01 3.67e-02 1.31e-03 30.32s
52000 +4.19507950e+04 +4.18687117e+04 +8.21e+01 4.05e-02 2.65e-03 32.53s
56000 +4.19510083e+04 +4.18951665e+04 +5.58e+01 3.67e-02 3.33e-01 34.75s
60000 +4.19508867e+04 +4.19031857e+04 +4.77e+01 2.64e-02 1.52e-03 36.96s
64000 +4.19502261e+04 +4.19103260e+04 +3.99e+01 2.44e-02 1.25e-03 39.18s
68000 +4.19505520e+04 +4.19165477e+04 +3.40e+01 2.03e-02 1.08e-03 41.39s
72000 +4.19510967e+04 +4.19211335e+04 +3.00e+01 2.19e-02 9.25e-04 43.61s
76000 +4.19509285e+04 +4.19249344e+04 +2.60e+01 1.64e-02 7.93e-04 45.82s
80000 +4.19510760e+04 +4.19055577e+04 +4.55e+01 2.56e-02 1.48e-03 48.04s
84000 +4.19506571e+04 +4.19217738e+04 +2.89e+01 1.92e-02 8.98e-04 50.25s
88000 +4.19508379e+04 +4.19269419e+04 +2.39e+01 1.67e-02 7.64e-04 52.47s
92000 +4.19508950e+04 +4.19301711e+04 +2.07e+01 1.52e-02 6.42e-04 54.68s
96000 +4.19509516e+04 +4.19322505e+04 +1.87e+01 1.42e-02 5.79e-04 56.90s
100000 +4.19510837e+04 +4.19340930e+04 +1.70e+01 1.26e-02 5.27e-04 59.12s
104000 +4.19508114e+04 +4.19355736e+04 +1.52e+01 1.19e-02 4.77e-04 61.34s
108000 +4.19508323e+04 +4.19366070e+04 +1.42e+01 1.02e-02 4.35e-04 63.56s
112000 +4.19507764e+04 +4.19381225e+04 +1.27e+01 9.66e-03 4.19e-04 65.79s
116000 +4.19510914e+04 +4.19389582e+04 +1.21e+01 1.01e-02 3.63e-04 68.02s
120000 +4.19509229e+04 +4.19401513e+04 +1.08e+01 9.40e-03 3.40e-04 70.25s
124000 +4.19508567e+04 +4.19402380e+04 +1.06e+01 7.96e-03 3.75e-04 72.49s
128000 +4.19508746e+04 +4.19446876e+04 +6.19e+00 6.75e-03 1.96e-04 74.72s
132000 +4.19507884e+04 +4.19456953e+04 +5.09e+00 6.51e-03 1.61e-04 76.95s
136000 +4.19508935e+04 +4.19462747e+04 +4.62e+00 6.52e-03 1.41e-04 79.18s
140000 +4.19508247e+04 +4.19466312e+04 +4.19e+00 6.01e-03 1.29e-04 81.42s
144000 +4.19507159e+04 +4.19470167e+04 +3.70e+00 6.23e-03 1.21e-04 83.65s
148000 +4.19508886e+04 +4.19471295e+04 +3.76e+00 4.95e-03 1.14e-04 85.88s
151800 +4.19508461e+04 +4.19500073e+04 +8.39e-01 7.02e-04 2.66e-05 88.00s
PDLP status: OPTIMAL
PDLP iterations: 151800
Primal objective: 4.19508461e+04
Dual objective: 4.19500073e+04
Primal infeasibility (abs/rel): 7.02e-04 / 6.34e-08
Dual infeasibility (abs/rel): 2.66e-05 / 3.06e-10
Duality gap (abs/rel): 8.39e-01 / 1.00e-05
Postsolving
Solving finished
Status: Optimal Objective: 4.1950846116e+04 Iterations: 151800(0) Time: 88.12s
COPT> set PDPTOL 1e-6
Unknown COPT parameter or attribute: PDPTOL
COPT> set PDlPTOL 1e-6
Setting parameter 'PDLPTol' to 1e-06
COPT> opt
Model fingerprint: 11cebb4f
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
14135 rows, 84693 columns and 11800327 non-zero elements
The presolved problem has:
13108 rows, 81336 columns and 11541827 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-04,5e-01]
Range of rhs coefficients: [1e-01,4e+00]
Range of bound coefficients: [2e-01,1e+02]
Range of cost coefficients: [9e-03,2e+04]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.11e+04 0.00e+00 3.79s
4000 +4.17407991e+04 +3.04897437e+04 +1.13e+04 2.98e+00 3.50e-01 6.27s
8000 +4.19070214e+04 +4.08247925e+04 +1.08e+03 1.13e+00 3.70e-02 8.45s
12000 +4.19414758e+04 +4.16358914e+04 +3.06e+02 4.70e-01 1.04e-02 10.64s
16000 +4.19482878e+04 +4.18529461e+04 +9.53e+01 1.90e-01 3.07e-03 12.83s
20000 +4.19509475e+04 +4.18808838e+04 +7.01e+01 1.31e-01 2.14e-03 15.05s
24000 +4.19503849e+04 +4.18968156e+04 +5.36e+01 8.06e-02 1.69e-03 17.30s
28000 +4.19513357e+04 +4.19022223e+04 +4.91e+01 6.54e-02 1.52e-03 19.51s
32000 +4.19500141e+04 +4.19077636e+04 +4.23e+01 5.78e-02 1.34e-03 21.70s
36000 +4.19503340e+04 +4.18930356e+04 +5.73e+01 4.79e-02 1.88e-03 23.93s
40000 +4.19512214e+04 +4.18980661e+04 +5.32e+01 4.64e-02 1.95e-03 26.19s
44000 +4.19517251e+04 +4.19044864e+04 +4.72e+01 4.24e-02 1.47e-03 28.43s
48000 +4.19519873e+04 +4.19109102e+04 +4.11e+01 3.67e-02 1.31e-03 30.63s
52000 +4.19507950e+04 +4.18687117e+04 +8.21e+01 4.05e-02 2.65e-03 32.87s
56000 +4.19510083e+04 +4.18951665e+04 +5.58e+01 3.67e-02 3.33e-01 35.15s
60000 +4.19508867e+04 +4.19031857e+04 +4.77e+01 2.64e-02 1.52e-03 37.42s
64000 +4.19502261e+04 +4.19103260e+04 +3.99e+01 2.44e-02 1.25e-03 39.63s
68000 +4.19505520e+04 +4.19165477e+04 +3.40e+01 2.03e-02 1.08e-03 41.87s
72000 +4.19510967e+04 +4.19211335e+04 +3.00e+01 2.19e-02 9.25e-04 44.16s
76000 +4.19509285e+04 +4.19249344e+04 +2.60e+01 1.64e-02 7.93e-04 46.43s
80000 +4.19510760e+04 +4.19055577e+04 +4.55e+01 2.56e-02 1.48e-03 48.65s
84000 +4.19506571e+04 +4.19217738e+04 +2.89e+01 1.92e-02 8.98e-04 50.88s
88000 +4.19508379e+04 +4.19269419e+04 +2.39e+01 1.67e-02 7.64e-04 53.17s
92000 +4.19508950e+04 +4.19301711e+04 +2.07e+01 1.52e-02 6.42e-04 55.44s
96000 +4.19509516e+04 +4.19322505e+04 +1.87e+01 1.42e-02 5.79e-04 57.67s
100000 +4.19510837e+04 +4.19340930e+04 +1.70e+01 1.26e-02 5.27e-04 59.90s
104000 +4.19508114e+04 +4.19355736e+04 +1.52e+01 1.19e-02 4.77e-04 62.20s
108000 +4.19508323e+04 +4.19366070e+04 +1.42e+01 1.02e-02 4.35e-04 64.50s
112000 +4.19507764e+04 +4.19381225e+04 +1.27e+01 9.66e-03 4.19e-04 66.73s
116000 +4.19510914e+04 +4.19389582e+04 +1.21e+01 1.01e-02 3.63e-04 68.97s
120000 +4.19509229e+04 +4.19401513e+04 +1.08e+01 9.40e-03 3.40e-04 71.27s
124000 +4.19508567e+04 +4.19402380e+04 +1.06e+01 7.96e-03 3.75e-04 73.57s
128000 +4.19508746e+04 +4.19446876e+04 +6.19e+00 6.75e-03 1.96e-04 75.81s
132000 +4.19507884e+04 +4.19456953e+04 +5.09e+00 6.51e-03 1.61e-04 78.04s
136000 +4.19508935e+04 +4.19462747e+04 +4.62e+00 6.52e-03 1.41e-04 80.35s
140000 +4.19508247e+04 +4.19466312e+04 +4.19e+00 6.01e-03 1.29e-04 82.65s
144000 +4.19507159e+04 +4.19470167e+04 +3.70e+00 6.23e-03 1.21e-04 84.89s
148000 +4.19508886e+04 +4.19471295e+04 +3.76e+00 4.95e-03 1.14e-04 87.12s
152000 +4.19508882e+04 +4.19474299e+04 +3.46e+00 5.94e-03 1.06e-04 89.42s
156000 +4.19507225e+04 +4.19474303e+04 +3.29e+00 4.48e-03 1.11e-04 91.73s
160000 +4.19508571e+04 +4.19476056e+04 +3.25e+00 5.01e-03 9.95e-05 93.97s
164000 +4.19509950e+04 +4.19476968e+04 +3.30e+00 4.79e-03 1.00e-04 96.21s
168000 +4.19509529e+04 +4.19478663e+04 +3.09e+00 4.70e-03 9.31e-05 98.50s
172000 +4.19508620e+04 +4.19479273e+04 +2.93e+00 3.99e-03 9.24e-05 100s
176000 +4.19507600e+04 +4.19480613e+04 +2.70e+00 4.59e-03 7.03e-03 103s
180000 +4.19509239e+04 +4.19481562e+04 +2.77e+00 4.17e-03 8.41e-05 105s
184000 +4.19508979e+04 +4.19482315e+04 +2.67e+00 3.92e-03 8.42e-05 107s
188000 +4.19508813e+04 +4.19483136e+04 +2.57e+00 4.21e-03 1.13e-04 109s
192000 +4.19508572e+04 +4.19487905e+04 +2.07e+00 2.65e-03 7.23e-05 112s
196000 +4.19508643e+04 +4.19493215e+04 +1.54e+00 2.82e-03 4.93e-05 114s
200000 +4.19508545e+04 +4.19494812e+04 +1.37e+00 2.43e-03 4.27e-05 117s
204000 +4.19508242e+04 +4.19496231e+04 +1.20e+00 2.41e-03 3.84e-05 119s
208000 +4.19508278e+04 +4.19497299e+04 +1.10e+00 2.33e-03 3.53e-05 122s
212000 +4.19508570e+04 +4.19497641e+04 +1.09e+00 2.14e-03 3.43e-05 124s
216000 +4.19508813e+04 +4.19498278e+04 +1.05e+00 2.27e-03 3.17e-05 127s
220000 +4.19508783e+04 +4.19498143e+04 +1.06e+00 2.03e-03 6.76e-05 130s
224000 +4.19509001e+04 +4.19499121e+04 +9.88e-01 2.38e-03 2.90e-05 132s
228000 +4.19508655e+04 +4.19499468e+04 +9.19e-01 2.06e-03 2.88e-05 135s
232000 +4.19508844e+04 +4.19499751e+04 +9.09e-01 2.24e-03 2.73e-05 138s
236000 +4.19508559e+04 +4.19499898e+04 +8.66e-01 2.06e-03 2.74e-05 140s
240000 +4.19508181e+04 +4.19500076e+04 +8.10e-01 1.79e-03 2.68e-05 143s
244000 +4.19507979e+04 +4.19500302e+04 +7.68e-01 2.04e-03 2.58e-05 146s
248000 +4.19508312e+04 +4.19500505e+04 +7.81e-01 1.80e-03 2.54e-05 148s
252000 +4.19508430e+04 +4.19500623e+04 +7.81e-01 1.68e-03 2.52e-05 151s
256000 +4.19508648e+04 +4.19500766e+04 +7.88e-01 1.54e-03 2.44e-05 154s
260000 +4.19508884e+04 +4.19500939e+04 +7.94e-01 1.87e-03 3.94e-05 156s
264000 +4.19508957e+04 +4.19500869e+04 +8.09e-01 1.65e-03 2.38e-05 159s
268000 +4.19508912e+04 +4.19501136e+04 +7.78e-01 1.64e-03 2.36e-05 162s
272000 +4.19508724e+04 +4.19501426e+04 +7.30e-01 1.68e-03 2.28e-05 164s
276000 +4.19508528e+04 +4.19499680e+04 +8.85e-01 1.60e-03 2.97e-05 167s
280000 +4.19508641e+04 +4.19502685e+04 +5.96e-01 1.23e-03 1.88e-05 170s
284000 +4.19508608e+04 +4.19503494e+04 +5.11e-01 1.08e-03 1.58e-05 172s
288000 +4.19508616e+04 +4.19504107e+04 +4.51e-01 1.20e-03 1.39e-05 175s
292000 +4.19508758e+04 +4.19504364e+04 +4.39e-01 1.08e-03 1.34e-05 178s
293600 +4.19508627e+04 +4.19507789e+04 +8.38e-02 3.67e-04 2.53e-06 179s
PDLP status: OPTIMAL
PDLP iterations: 293600
Primal objective: 4.19508627e+04
Dual objective: 4.19507789e+04
Primal infeasibility (abs/rel): 3.67e-04 / 3.32e-08
Dual infeasibility (abs/rel): 2.53e-06 / 2.91e-11
Duality gap (abs/rel): 8.38e-02 / 9.99e-07
Postsolving
Solving finished
Status: Optimal Objective: 4.1950862671e+04 Iterations: 293600(0) Time: 179.44s
COPT> read instance23.mps
Reading from 'C:\Users\.PC\highs_test\instance23.mps'
Reading finished (0.17s)
COPT> set pdlptol 1e-4
Setting parameter 'PDLPTol' to 0.0001
COPT> opt
Model fingerprint: 248df987
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
The presolved problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,1e-01]
Range of rhs coefficients: [3e-02,4e-01]
Range of bound coefficients: [9e+00,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.23e+02 0.00e+00 0.61s
4000 +2.46566700e+04 +1.81763172e+03 +2.28e+04 3.49e-01 9.43e+00 1.65s
8000 +1.66667109e+04 -1.86688127e+05 +2.03e+05 2.07e-01 1.15e+02 2.35s
12000 +1.72031344e+04 +8.27048575e+03 +8.93e+03 3.71e-02 1.85e+01 3.04s
16000 +1.72518962e+04 +1.31211733e+04 +4.13e+03 7.50e-03 2.73e+00 3.72s
20000 +1.73959722e+04 +1.50873761e+04 +2.31e+03 2.77e-03 2.32e+00 4.43s
24000 +1.69183399e+04 +1.67131181e+04 +2.05e+02 2.98e-01 6.12e-01 5.12s
28000 +1.67208817e+04 +1.72665395e+04 +5.46e+02 4.30e-02 1.17e-02 5.82s
32000 +1.69293086e+04 +1.72817667e+04 +3.52e+02 7.34e-02 8.22e-03 6.51s
36000 +1.70278015e+04 +1.72779332e+04 +2.50e+02 1.68e-02 3.97e-03 7.19s
40000 +1.71233898e+04 +1.72770942e+04 +1.54e+02 1.10e-02 4.37e-03 7.88s
42640 +1.72723104e+04 +1.72742833e+04 +1.97e+00 5.24e-03 4.30e-03 8.35s
PDLP status: OPTIMAL
PDLP iterations: 42640
Primal objective: 1.72723104e+04
Dual objective: 1.72742833e+04
Primal infeasibility (abs/rel): 5.24e-03 / 2.34e-05
Dual infeasibility (abs/rel): 4.30e-03 / 5.29e-07
Duality gap (abs/rel): 1.97e+00 / 5.71e-05
Solving finished
Status: Optimal Objective: 1.7272310363e+04 Iterations: 42640(0) Time: 8.41s
COPT> set pdlptol 1e-5
Setting parameter 'PDLPTol' to 1e-05
COPT> opt
Model fingerprint: 248df987
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
The presolved problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,1e-01]
Range of rhs coefficients: [3e-02,4e-01]
Range of bound coefficients: [9e+00,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.23e+02 0.00e+00 0.62s
4000 +2.46566700e+04 +1.81763172e+03 +2.28e+04 3.49e-01 9.43e+00 1.62s
8000 +1.66667109e+04 -1.86688127e+05 +2.03e+05 2.07e-01 1.15e+02 2.31s
12000 +1.72031344e+04 +8.27048575e+03 +8.93e+03 3.71e-02 1.85e+01 3.00s
16000 +1.72518962e+04 +1.31211733e+04 +4.13e+03 7.50e-03 2.73e+00 3.70s
20000 +1.73959722e+04 +1.50873761e+04 +2.31e+03 2.77e-03 2.32e+00 4.40s
24000 +1.69183399e+04 +1.67131181e+04 +2.05e+02 2.98e-01 6.12e-01 5.10s
28000 +1.67208817e+04 +1.72665395e+04 +5.46e+02 4.30e-02 1.17e-02 5.80s
32000 +1.69293086e+04 +1.72817667e+04 +3.52e+02 7.34e-02 8.22e-03 6.49s
36000 +1.70278015e+04 +1.72779332e+04 +2.50e+02 1.68e-02 3.97e-03 7.18s
40000 +1.71233898e+04 +1.72770942e+04 +1.54e+02 1.10e-02 4.37e-03 7.87s
44000 +1.72741397e+04 +1.72814089e+04 +7.27e+00 3.25e-03 1.69e-03 8.57s
44320 +1.72816027e+04 +1.72813226e+04 +2.80e-01 1.81e-03 1.36e-03 8.63s
PDLP status: OPTIMAL
PDLP iterations: 44320
Primal objective: 1.72816027e+04
Dual objective: 1.72813226e+04
Primal infeasibility (abs/rel): 1.81e-03 / 8.07e-06
Dual infeasibility (abs/rel): 1.36e-03 / 1.67e-07
Duality gap (abs/rel): 2.80e-01 / 8.10e-06
Solving finished
Status: Optimal Objective: 1.7281602707e+04 Iterations: 44320(0) Time: 8.68s
COPT> set pdlptol 1e-6
Setting parameter 'PDLPTol' to 1e-06
COPT> opt
Model fingerprint: 248df987
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
The presolved problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,1e-01]
Range of rhs coefficients: [3e-02,4e-01]
Range of bound coefficients: [9e+00,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.23e+02 0.00e+00 0.61s
4000 +2.46566700e+04 +1.81763172e+03 +2.28e+04 3.49e-01 9.43e+00 1.53s
8000 +1.66667109e+04 -1.86688127e+05 +2.03e+05 2.07e-01 1.15e+02 2.24s
12000 +1.72031344e+04 +8.27048575e+03 +8.93e+03 3.71e-02 1.85e+01 2.94s
16000 +1.72518962e+04 +1.31211733e+04 +4.13e+03 7.50e-03 2.73e+00 3.64s
20000 +1.73959722e+04 +1.50873761e+04 +2.31e+03 2.77e-03 2.32e+00 4.33s
24000 +1.69183399e+04 +1.67131181e+04 +2.05e+02 2.98e-01 6.12e-01 5.03s
28000 +1.67208817e+04 +1.72665395e+04 +5.46e+02 4.30e-02 1.17e-02 5.73s
32000 +1.69293086e+04 +1.72817667e+04 +3.52e+02 7.34e-02 8.22e-03 6.42s
36000 +1.70278015e+04 +1.72779332e+04 +2.50e+02 1.68e-02 3.97e-03 7.11s
40000 +1.71233898e+04 +1.72770942e+04 +1.54e+02 1.10e-02 4.37e-03 7.80s
44000 +1.72741397e+04 +1.72814089e+04 +7.27e+00 3.25e-03 1.69e-03 8.50s
48000 +1.72820303e+04 +1.72836364e+04 +1.61e+00 5.20e-04 9.64e-04 9.19s
49720 +1.72835358e+04 +1.72835275e+04 +8.21e-03 2.04e-04 4.76e-04 9.49s
PDLP status: OPTIMAL
PDLP iterations: 49720
Primal objective: 1.72835358e+04
Dual objective: 1.72835275e+04
Primal infeasibility (abs/rel): 2.04e-04 / 9.08e-07
Dual infeasibility (abs/rel): 4.76e-04 / 5.85e-08
Duality gap (abs/rel): 8.21e-03 / 2.38e-07
Solving finished
Status: Optimal Objective: 1.7283535760e+04 Iterations: 49720(0) Time: 9.54s
COPT> read instance22.mps
Reading from 'C:\Users\.PC\highs_test\instance22.mps'
Reading finished (0.10s)
COPT> opt
Model fingerprint: 44bcbef1
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
The presolved problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,2e-01]
Range of rhs coefficients: [2e-02,5e-01]
Range of bound coefficients: [1e+01,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.71e+02 0.00e+00 0.41s
4000 +2.98256689e+04 +1.56206119e+04 +1.42e+04 2.49e-01 2.16e+01 1.16s
8000 +3.07125175e+04 +2.86771525e+04 +2.04e+03 2.87e-02 1.32e+00 1.64s
12000 +3.07596000e+04 +2.78594921e+04 +2.90e+03 2.92e-02 9.50e-01 2.14s
16000 +3.04498009e+04 +2.91989035e+04 +1.25e+03 1.24e-02 1.28e+00 2.63s
20000 +3.01873180e+04 +2.97569127e+04 +4.30e+02 5.46e-03 3.70e-01 3.13s
24000 +3.02484546e+04 +2.99559857e+04 +2.92e+02 2.82e-03 2.14e-01 3.62s
28000 +3.02375446e+04 +3.00484188e+04 +1.89e+02 3.19e-03 1.49e-01 4.12s
32000 +3.02143422e+04 +3.02026327e+04 +1.17e+01 2.64e-02 3.20e-02 4.61s
36000 +3.02198688e+04 +3.02345840e+04 +1.47e+01 2.81e-02 4.44e-03 5.10s
40000 +3.02216157e+04 +3.02374384e+04 +1.58e+01 1.21e-02 1.68e-03 5.58s
44000 +3.02312188e+04 +3.02381203e+04 +6.90e+00 6.04e-03 1.05e-03 6.08s
48000 +3.02352213e+04 +3.02386016e+04 +3.38e+00 4.15e-03 5.76e-04 6.57s
52000 +3.02360742e+04 +3.02387673e+04 +2.69e+00 2.71e-03 3.79e-04 7.06s
56000 +3.02432316e+04 +3.02390450e+04 +4.19e+00 1.88e-02 1.22e-04 7.55s
60000 +3.02508121e+04 +3.02391127e+04 +1.17e+01 1.02e-02 4.53e-05 8.04s
64000 +3.02448143e+04 +3.02391252e+04 +5.69e+00 6.50e-03 3.02e-05 8.52s
68000 +3.02433527e+04 +3.02391350e+04 +4.22e+00 5.17e-03 1.86e-05 9.01s
72000 +3.02428267e+04 +3.02391380e+04 +3.69e+00 4.32e-03 1.53e-05 9.49s
76000 +3.02428937e+04 +3.02391397e+04 +3.75e+00 3.65e-03 1.44e-05 9.98s
80000 +3.02422458e+04 +3.02391455e+04 +3.10e+00 3.21e-03 1.23e-05 10.47s
84000 +3.02409941e+04 +3.02391506e+04 +1.84e+00 4.50e-03 1.29e-05 10.95s
88000 +3.02409958e+04 +3.02391423e+04 +1.85e+00 2.43e-03 1.10e-05 11.44s
92000 +3.02414133e+04 +3.02391419e+04 +2.27e+00 2.25e-03 1.03e-05 11.92s
96000 +3.02412415e+04 +3.02391448e+04 +2.10e+00 2.19e-03 8.50e-06 12.41s
100000 +3.02404016e+04 +3.02391419e+04 +1.26e+00 1.93e-03 1.15e-05 12.91s
104000 +3.02403034e+04 +3.02391415e+04 +1.16e+00 1.78e-03 1.16e-05 13.40s
108000 +3.02410015e+04 +3.02391348e+04 +1.87e+00 1.27e-03 1.83e-05 13.89s
112000 +3.02399650e+04 +3.02391345e+04 +8.30e-01 1.04e-03 1.81e-05 14.38s
116000 +3.02395849e+04 +3.02391382e+04 +4.47e-01 9.63e-04 1.44e-05 14.88s
120000 +3.02395124e+04 +3.02391380e+04 +3.74e-01 7.89e-04 1.45e-05 15.37s
124000 +3.02393583e+04 +3.02391336e+04 +2.25e-01 6.35e-04 1.81e-05 15.86s
128000 +3.02390860e+04 +3.02391403e+04 +5.43e-02 4.33e-03 5.78e-05 16.36s
132000 +3.02386995e+04 +3.02391309e+04 +4.31e-01 3.43e-04 2.00e-05 16.85s
136000 +3.02388551e+04 +3.02391346e+04 +2.79e-01 4.14e-04 1.67e-05 17.35s
140000 +3.02391117e+04 +3.02391395e+04 +2.78e-02 5.07e-04 1.28e-05 17.83s
144000 +3.02392327e+04 +3.02391401e+04 +9.26e-02 4.80e-04 1.18e-05 18.33s
148000 +3.02391362e+04 +3.02391376e+04 +1.36e-03 3.32e-04 1.44e-05 18.83s
152000 +3.02389536e+04 +3.02391385e+04 +1.85e-01 2.43e-04 1.31e-05 19.32s
156000 +3.02390341e+04 +3.02391413e+04 +1.07e-01 2.63e-04 1.12e-05 19.81s
160000 +3.02389831e+04 +3.02391433e+04 +1.60e-01 2.66e-04 9.15e-06 20.30s
164000 +3.02392472e+04 +3.02391430e+04 +1.04e-01 2.18e-04 9.48e-06 20.80s
168000 +3.02392566e+04 +3.02391429e+04 +1.14e-01 1.72e-04 9.43e-06 21.29s
172000 +3.02393400e+04 +3.02391444e+04 +1.96e-01 1.93e-04 7.67e-06 21.78s
176000 +3.02392110e+04 +3.02391475e+04 +6.35e-02 2.59e-04 4.97e-06 22.28s
180000 +3.02390980e+04 +3.02391512e+04 +5.32e-02 3.71e-04 7.28e-06 22.78s
184000 +3.02390655e+04 +3.02391450e+04 +7.96e-02 1.52e-04 6.77e-06 23.26s
184560 +3.02390878e+04 +3.02391451e+04 +5.73e-02 1.52e-04 6.57e-06 23.34s
PDLP status: OPTIMAL
PDLP iterations: 184560
Primal objective: 3.02390878e+04
Dual objective: 3.02391451e+04
Primal infeasibility (abs/rel): 1.52e-04 / 8.88e-07
Dual infeasibility (abs/rel): 6.57e-06 / 1.08e-09
Duality gap (abs/rel): 5.73e-02 / 9.48e-07
Solving finished
Status: Optimal Objective: 3.0239087824e+04 Iterations: 184560(0) Time: 23.39s
COPT> set pdlptol 1e-5
Setting parameter 'PDLPTol' to 1e-05
COPT> opt
Model fingerprint: 44bcbef1
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
The presolved problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,2e-01]
Range of rhs coefficients: [2e-02,5e-01]
Range of bound coefficients: [1e+01,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.71e+02 0.00e+00 0.42s
4000 +2.98256689e+04 +1.56206119e+04 +1.42e+04 2.49e-01 2.16e+01 1.22s
8000 +3.07125175e+04 +2.86771525e+04 +2.04e+03 2.87e-02 1.32e+00 1.71s
12000 +3.07596000e+04 +2.78594921e+04 +2.90e+03 2.92e-02 9.50e-01 2.21s
16000 +3.04498009e+04 +2.91989035e+04 +1.25e+03 1.24e-02 1.28e+00 2.71s
20000 +3.01873180e+04 +2.97569127e+04 +4.30e+02 5.46e-03 3.70e-01 3.21s
24000 +3.02484546e+04 +2.99559857e+04 +2.92e+02 2.82e-03 2.14e-01 3.69s
28000 +3.02375446e+04 +3.00484188e+04 +1.89e+02 3.19e-03 1.49e-01 4.19s
32000 +3.02143422e+04 +3.02026327e+04 +1.17e+01 2.64e-02 3.20e-02 4.69s
36000 +3.02198688e+04 +3.02345840e+04 +1.47e+01 2.81e-02 4.44e-03 5.17s
40000 +3.02216157e+04 +3.02374384e+04 +1.58e+01 1.21e-02 1.68e-03 5.67s
44000 +3.02312188e+04 +3.02381203e+04 +6.90e+00 6.04e-03 1.05e-03 6.17s
48000 +3.02352213e+04 +3.02386016e+04 +3.38e+00 4.15e-03 5.76e-04 6.66s
52000 +3.02360742e+04 +3.02387673e+04 +2.69e+00 2.71e-03 3.79e-04 7.15s
56000 +3.02432316e+04 +3.02390450e+04 +4.19e+00 1.88e-02 1.22e-04 7.64s
60000 +3.02508121e+04 +3.02391127e+04 +1.17e+01 1.02e-02 4.53e-05 8.14s
64000 +3.02448143e+04 +3.02391252e+04 +5.69e+00 6.50e-03 3.02e-05 8.62s
68000 +3.02433527e+04 +3.02391350e+04 +4.22e+00 5.17e-03 1.86e-05 9.13s
72000 +3.02428267e+04 +3.02391380e+04 +3.69e+00 4.32e-03 1.53e-05 9.62s
76000 +3.02428937e+04 +3.02391397e+04 +3.75e+00 3.65e-03 1.44e-05 10.11s
80000 +3.02422458e+04 +3.02391455e+04 +3.10e+00 3.21e-03 1.23e-05 10.60s
84000 +3.02409941e+04 +3.02391506e+04 +1.84e+00 4.50e-03 1.29e-05 11.09s
88000 +3.02409958e+04 +3.02391423e+04 +1.85e+00 2.43e-03 1.10e-05 11.58s
92000 +3.02414133e+04 +3.02391419e+04 +2.27e+00 2.25e-03 1.03e-05 12.07s
96000 +3.02412415e+04 +3.02391448e+04 +2.10e+00 2.19e-03 8.50e-06 12.56s
100000 +3.02404016e+04 +3.02391419e+04 +1.26e+00 1.93e-03 1.15e-05 13.06s
104000 +3.02403034e+04 +3.02391415e+04 +1.16e+00 1.78e-03 1.16e-05 13.55s
108000 +3.02410015e+04 +3.02391348e+04 +1.87e+00 1.27e-03 1.83e-05 14.04s
112000 +3.02399650e+04 +3.02391345e+04 +8.30e-01 1.04e-03 1.81e-05 14.53s
113480 +3.02396963e+04 +3.02391357e+04 +5.61e-01 9.95e-04 1.68e-05 14.72s
PDLP status: OPTIMAL
PDLP iterations: 113480
Primal objective: 3.02396963e+04
Dual objective: 3.02391357e+04
Primal infeasibility (abs/rel): 9.95e-04 / 5.80e-06
Dual infeasibility (abs/rel): 1.68e-05 / 2.75e-09
Duality gap (abs/rel): 5.61e-01 / 9.27e-06
Solving finished
Status: Optimal Objective: 3.0239696327e+04 Iterations: 113480(0) Time: 14.77s
COPT> set pdlptol 1e-4
Setting parameter 'PDLPTol' to 0.0001
COPT> opt
Model fingerprint: 44bcbef1
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
The presolved problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [2e-03,2e-01]
Range of rhs coefficients: [2e-02,5e-01]
Range of bound coefficients: [1e+01,2e+01]
Range of cost coefficients: [7e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 1.71e+02 0.00e+00 0.41s
4000 +2.98256689e+04 +1.56206119e+04 +1.42e+04 2.49e-01 2.16e+01 1.22s
8000 +3.07125175e+04 +2.86771525e+04 +2.04e+03 2.87e-02 1.32e+00 1.71s
12000 +3.07596000e+04 +2.78594921e+04 +2.90e+03 2.92e-02 9.50e-01 2.22s
16000 +3.04498009e+04 +2.91989035e+04 +1.25e+03 1.24e-02 1.28e+00 2.71s
20000 +3.01873180e+04 +2.97569127e+04 +4.30e+02 5.46e-03 3.70e-01 3.20s
24000 +3.02484546e+04 +2.99559857e+04 +2.92e+02 2.82e-03 2.14e-01 3.70s
28000 +3.02375446e+04 +3.00484188e+04 +1.89e+02 3.19e-03 1.49e-01 4.19s
32000 +3.02143422e+04 +3.02026327e+04 +1.17e+01 2.64e-02 3.20e-02 4.69s
33800 +3.02266059e+04 +3.02237759e+04 +2.83e+00 1.71e-02 1.35e-02 4.91s
PDLP status: OPTIMAL
PDLP iterations: 33800
Primal objective: 3.02266059e+04
Dual objective: 3.02237759e+04
Primal infeasibility (abs/rel): 1.71e-02 / 9.98e-05
Dual infeasibility (abs/rel): 1.35e-02 / 2.21e-06
Duality gap (abs/rel): 2.83e+00 / 4.68e-05
Solving finished
Status: Optimal Objective: 3.0226605881e+04 Iterations: 33800(0) Time: 4.96s
COPT> read instance21.mps
Reading from 'C:\Users\.PC\highs_test\instance21.mps'
Reading finished (0.03s)
COPT> opt
Model fingerprint: 8d056eaa
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
1556 rows, 9235 columns and 603232 non-zero elements
The presolved problem has:
1556 rows, 9235 columns and 603232 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-03,1e-01]
Range of rhs coefficients: [9e-02,9e-01]
Range of bound coefficients: [7e+00,1e+01]
Range of cost coefficients: [9e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.36e+02 0.00e+00 0.19s
4000 +2.23292760e+04 +1.68663408e+04 +5.46e+03 1.57e-01 2.34e+01 0.74s
8000 +2.15327786e+04 +2.06300229e+04 +9.03e+02 6.57e-02 2.10e+00 0.99s
12000 +2.12253136e+04 +2.11081129e+04 +1.17e+02 6.27e-01 1.05e-01 1.24s
13200 +2.11208830e+04 +2.11212373e+04 +3.54e-01 8.80e-03 1.15e-02 1.33s
PDLP status: OPTIMAL
PDLP iterations: 13200
Primal objective: 2.11208830e+04
Dual objective: 2.11212373e+04
Primal infeasibility (abs/rel): 8.80e-03 / 3.71e-05
Dual infeasibility (abs/rel): 1.15e-02 / 2.90e-06
Duality gap (abs/rel): 3.54e-01 / 8.39e-06
Solving finished
Status: Optimal Objective: 2.1120883035e+04 Iterations: 13200(0) Time: 1.37s
COPT> set pdlptol 1e-5
Setting parameter 'PDLPTol' to 1e-05
COPT> opt
Model fingerprint: 8d056eaa
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
1556 rows, 9235 columns and 603232 non-zero elements
The presolved problem has:
1556 rows, 9235 columns and 603232 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-03,1e-01]
Range of rhs coefficients: [9e-02,9e-01]
Range of bound coefficients: [7e+00,1e+01]
Range of cost coefficients: [9e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.36e+02 0.00e+00 0.19s
4000 +2.23292760e+04 +1.68663408e+04 +5.46e+03 1.57e-01 2.34e+01 0.78s
8000 +2.15327786e+04 +2.06300229e+04 +9.03e+02 6.57e-02 2.10e+00 1.03s
12000 +2.12253136e+04 +2.11081129e+04 +1.17e+02 6.27e-01 1.05e-01 1.29s
16000 +2.11513432e+04 +2.11281016e+04 +2.32e+01 3.99e-03 1.35e-02 1.55s
18440 +2.11295378e+04 +2.11291623e+04 +3.76e-01 2.23e-03 7.55e-03 1.71s
PDLP status: OPTIMAL
PDLP iterations: 18440
Primal objective: 2.11295378e+04
Dual objective: 2.11291623e+04
Primal infeasibility (abs/rel): 2.23e-03 / 9.41e-06
Dual infeasibility (abs/rel): 7.55e-03 / 1.91e-06
Duality gap (abs/rel): 3.76e-01 / 8.89e-06
Solving finished
Status: Optimal Objective: 2.1129537831e+04 Iterations: 18440(0) Time: 1.76s
COPT> set pdlptol 1e-6
Setting parameter 'PDLPTol' to 1e-06
COPT> opt
Model fingerprint: 8d056eaa
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
1556 rows, 9235 columns and 603232 non-zero elements
The presolved problem has:
1556 rows, 9235 columns and 603232 non-zero elements
Hardware has 1 supported GPU device with CUDA 12.8
GPU 0: NVIDIA GeForce RTX 3080 (CUDA capability 8.6)
Starting PDLP solver using GPU 0
Problem info:
Range of matrix coefficients: [3e-03,1e-01]
Range of rhs coefficients: [9e-02,9e-01]
Range of bound coefficients: [7e+00,1e+01]
Range of cost coefficients: [9e-02,1e+02]
Iterations Primal.Obj Dual.Obj Gap Primal.Inf Dual.Inf Time
0 +0.00000000e+00 +0.00000000e+00 +0.00e+00 2.36e+02 0.00e+00 0.19s
4000 +2.23292760e+04 +1.68663408e+04 +5.46e+03 1.57e-01 2.34e+01 0.64s
8000 +2.15327786e+04 +2.06300229e+04 +9.03e+02 6.57e-02 2.10e+00 0.89s
12000 +2.12253136e+04 +2.11081129e+04 +1.17e+02 6.27e-01 1.05e-01 1.16s
16000 +2.11513432e+04 +2.11281016e+04 +2.32e+01 3.99e-03 1.35e-02 1.41s
20000 +2.11467450e+04 +2.11298972e+04 +1.68e+01 2.44e-03 2.85e-03 1.68s
24000 +2.11562881e+04 +2.11319121e+04 +2.44e+01 4.38e-03 2.12e-03 1.94s
28000 +2.11015027e+04 +2.11322662e+04 +3.08e+01 4.28e-03 1.42e-04 2.19s
32000 +2.11495696e+04 +2.11321094e+04 +1.75e+01 2.28e-03 2.43e-04 2.44s
36000 +2.11325875e+04 +2.11323206e+04 +2.67e-01 1.45e-04 5.75e-05 2.69s
36080 +2.11323351e+04 +2.11323159e+04 +1.91e-02 1.20e-04 5.97e-05 2.70s
PDLP status: OPTIMAL
PDLP iterations: 36080
Primal objective: 2.11323351e+04
Dual objective: 2.11323159e+04
Primal infeasibility (abs/rel): 1.20e-04 / 5.06e-07
Dual infeasibility (abs/rel): 5.97e-05 / 1.51e-08
Duality gap (abs/rel): 1.91e-02 / 4.53e-07
Solving finished
Status: Optimal Objective: 2.1132335057e+04 Iterations: 36080(0) Time: 2.75s
COPT>
@PC:~/cuPDLPx-main/cuPDLPx-main/build$ ./cupdlpx --verbose --eps_opt 1e-6 instance24.mps log
---------------------------------------------------------------------------------------
cuPDLPx v0.1.4
A GPU-Accelerated First-Order LP Solver
(c) Haihao Lu, Massachusetts Institute of Technology, 2025
---------------------------------------------------------------------------------------
problem:
variables : 84693
constraints : 14135
nnz(A) : 11800327
settings:
iter_limit : 2147483647
time_limit : 3600.00 sec
eps_opt : 1.0e-06
eps_feas : 1.0e-04
eps_infeas_detect : 1.0e-10
---------------------------------------------------------------------------------------
runtime | objective | absolute residuals | relative residuals
iter time | pr obj du obj | pr res du res gap | pr res du res gap
---------------------------------------------------------------------------------------
0 1.0e-03 | 0.0e+00 0.0e+00 | 1.1e+04 2.0e+04 0.0e+00 | 1.0e+00 1.0e+00 0.0e+00
10 8.6e-03 | 7.4e+05 1.0e+07 | 2.9e+03 1.5e+06 9.6e+06 | 2.6e-01 7.5e+01 8.7e-01
20 1.7e-02 | 8.0e+05 5.8e+06 | 1.6e+03 9.2e+05 5.0e+06 | 1.4e-01 4.5e+01 7.6e-01
30 2.3e-02 | 4.2e+05 4.9e+06 | 4.1e+02 6.7e+05 4.5e+06 | 3.7e-02 3.3e+01 8.4e-01
40 3.0e-02 | 2.4e+05 3.4e+06 | 3.9e+02 5.1e+05 3.1e+06 | 3.5e-02 2.5e+01 8.6e-01
50 3.6e-02 | 1.9e+05 2.3e+06 | 3.7e+02 3.9e+05 2.1e+06 | 3.4e-02 1.9e+01 8.4e-01
60 4.3e-02 | 1.9e+05 1.8e+06 | 2.3e+02 3.3e+05 1.6e+06 | 2.1e-02 1.6e+01 8.1e-01
70 5.1e-02 | 1.6e+05 1.7e+06 | 2.4e+02 3.1e+05 1.5e+06 | 2.2e-02 1.5e+01 8.3e-01
80 5.7e-02 | 1.3e+05 1.7e+06 | 2.2e+02 3.0e+05 1.5e+06 | 2.0e-02 1.5e+01 8.5e-01
90 6.3e-02 | 1.4e+05 1.5e+06 | 1.3e+02 2.8e+05 1.4e+06 | 1.2e-02 1.4e+01 8.3e-01
100 7.0e-02 | 1.6e+05 1.3e+06 | 1.1e+02 2.5e+05 1.2e+06 | 9.9e-03 1.2e+01 7.9e-01
110 7.8e-02 | 1.4e+05 1.2e+06 | 1.0e+02 2.2e+05 1.0e+06 | 9.2e-03 1.1e+01 7.8e-01
120 8.4e-02 | 1.3e+05 1.1e+06 | 8.7e+01 2.0e+05 9.3e+05 | 7.8e-03 1.0e+01 7.9e-01
130 9.1e-02 | 1.2e+05 1.0e+06 | 1.1e+02 1.9e+05 8.8e+05 | 1.0e-02 9.5e+00 7.8e-01
140 9.7e-02 | 1.2e+05 9.9e+05 | 9.8e+01 1.9e+05 8.6e+05 | 8.9e-03 9.2e+00 7.8e-01
150 1.0e-01 | 1.2e+05 9.4e+05 | 6.8e+01 1.8e+05 8.2e+05 | 6.1e-03 8.7e+00 7.7e-01
160 1.1e-01 | 1.2e+05 8.7e+05 | 5.0e+01 1.6e+05 7.5e+05 | 4.5e-03 8.1e+00 7.6e-01
170 1.2e-01 | 1.1e+05 8.0e+05 | 4.4e+01 1.5e+05 6.9e+05 | 4.0e-03 7.6e+00 7.5e-01
180 1.2e-01 | 1.1e+05 7.7e+05 | 5.7e+01 1.5e+05 6.6e+05 | 5.2e-03 7.2e+00 7.5e-01
190 1.3e-01 | 1.1e+05 7.5e+05 | 5.7e+01 1.4e+05 6.5e+05 | 5.2e-03 7.0e+00 7.5e-01
200 1.4e-01 | 1.0e+05 7.3e+05 | 4.7e+01 1.4e+05 6.3e+05 | 4.3e-03 6.7e+00 7.5e-01
210 1.5e-01 | 1.1e+05 3.6e+05 | 5.5e+02 1.0e+05 2.5e+05 | 5.0e-02 4.9e+00 5.3e-01
220 1.5e-01 | 1.1e+05 1.9e+05 | 7.3e+02 8.7e+04 7.8e+04 | 6.6e-02 4.3e+00 2.6e-01
230 1.6e-01 | 1.1e+05 1.3e+05 | 5.3e+02 7.4e+04 2.2e+04 | 4.8e-02 3.6e+00 8.9e-02
240 1.7e-01 | 9.7e+04 1.2e+05 | 3.4e+02 6.4e+04 2.7e+04 | 3.0e-02 3.2e+00 1.2e-01
250 1.7e-01 | 9.0e+04 1.4e+05 | 3.2e+02 5.7e+04 4.9e+04 | 2.9e-02 2.8e+00 2.2e-01
260 1.8e-01 | 8.7e+04 1.3e+05 | 3.7e+02 5.2e+04 4.4e+04 | 3.3e-02 2.6e+00 2.0e-01
270 1.9e-01 | 8.6e+04 1.1e+05 | 3.6e+02 4.7e+04 2.1e+04 | 3.2e-02 2.3e+00 1.1e-01
280 1.9e-01 | 8.8e+04 9.7e+04 | 3.0e+02 4.3e+04 8.9e+03 | 2.7e-02 2.1e+00 4.9e-02
290 2.0e-01 | 8.7e+04 1.0e+05 | 2.7e+02 3.9e+04 1.3e+04 | 2.4e-02 1.9e+00 7.1e-02
300 2.1e-01 | 8.5e+04 1.0e+05 | 2.7e+02 3.6e+04 1.6e+04 | 2.5e-02 1.8e+00 8.8e-02
310 2.1e-01 | 8.3e+04 9.3e+04 | 2.7e+02 3.4e+04 1.0e+04 | 2.5e-02 1.7e+00 5.8e-02
320 2.2e-01 | 8.3e+04 8.6e+04 | 2.5e+02 3.1e+04 2.9e+03 | 2.2e-02 1.5e+00 1.7e-02
330 2.3e-01 | 8.3e+04 8.8e+04 | 2.1e+02 2.9e+04 5.1e+03 | 1.9e-02 1.4e+00 3.0e-02
340 2.3e-01 | 8.2e+04 9.0e+04 | 2.1e+02 2.8e+04 8.0e+03 | 1.9e-02 1.4e+00 4.7e-02
350 2.4e-01 | 8.0e+04 8.6e+04 | 2.2e+02 2.6e+04 6.0e+03 | 2.0e-02 1.3e+00 3.6e-02
360 2.5e-01 | 7.9e+04 8.2e+04 | 2.0e+02 2.4e+04 2.4e+03 | 1.8e-02 1.2e+00 1.5e-02
370 2.5e-01 | 7.9e+04 8.1e+04 | 1.8e+02 2.3e+04 2.4e+03 | 1.6e-02 1.2e+00 1.5e-02
380 2.6e-01 | 7.8e+04 8.3e+04 | 1.7e+02 2.2e+04 4.9e+03 | 1.6e-02 1.1e+00 3.0e-02
390 2.7e-01 | 7.6e+04 8.0e+04 | 1.7e+02 2.1e+04 3.6e+03 | 1.6e-02 1.1e+00 2.3e-02
400 2.8e-01 | 7.6e+04 7.8e+04 | 1.6e+02 2.0e+04 2.1e+03 | 1.5e-02 1.0e+00 1.3e-02
410 2.8e-01 | 7.5e+04 6.4e+04 | 1.6e+02 1.8e+04 1.1e+04 | 1.4e-02 9.0e-01 8.1e-02
420 2.9e-01 | 7.5e+04 6.2e+04 | 1.4e+02 1.8e+04 1.3e+04 | 1.3e-02 8.8e-01 9.6e-02
430 3.0e-01 | 7.5e+04 6.2e+04 | 1.3e+02 1.8e+04 1.2e+04 | 1.2e-02 8.7e-01 9.0e-02
440 3.0e-01 | 7.4e+04 6.2e+04 | 1.3e+02 1.8e+04 1.2e+04 | 1.2e-02 8.7e-01 8.5e-02
450 3.1e-01 | 7.3e+04 6.1e+04 | 1.3e+02 1.8e+04 1.2e+04 | 1.1e-02 8.7e-01 9.1e-02
460 3.2e-01 | 7.2e+04 5.9e+04 | 1.2e+02 1.7e+04 1.3e+04 | 1.1e-02 8.6e-01 9.9e-02
470 3.2e-01 | 7.1e+04 5.9e+04 | 1.1e+02 1.7e+04 1.2e+04 | 1.0e-02 8.5e-01 9.2e-02
480 3.3e-01 | 7.0e+04 6.0e+04 | 1.1e+02 1.7e+04 1.1e+04 | 9.6e-03 8.4e-01 8.1e-02
490 3.4e-01 | 7.0e+04 6.0e+04 | 1.0e+02 1.7e+04 9.6e+03 | 9.3e-03 8.2e-01 7.4e-02
500 3.4e-01 | 6.9e+04 6.0e+04 | 9.9e+01 1.6e+04 9.0e+03 | 9.0e-03 8.1e-01 7.0e-02
510 3.5e-01 | 6.8e+04 6.0e+04 | 9.5e+01 1.6e+04 7.9e+03 | 8.6e-03 7.9e-01 6.1e-02
520 3.6e-01 | 6.8e+04 6.1e+04 | 9.2e+01 1.6e+04 6.7e+03 | 8.3e-03 7.7e-01 5.2e-02
530 3.6e-01 | 6.7e+04 6.1e+04 | 8.9e+01 1.5e+04 6.0e+03 | 8.0e-03 7.6e-01 4.7e-02
540 3.7e-01 | 6.6e+04 6.1e+04 | 8.6e+01 1.5e+04 5.3e+03 | 7.8e-03 7.4e-01 4.2e-02
550 3.7e-01 | 6.5e+04 6.1e+04 | 8.3e+01 1.5e+04 4.4e+03 | 7.5e-03 7.2e-01 3.4e-02
560 3.8e-01 | 6.5e+04 6.1e+04 | 7.9e+01 1.4e+04 3.6e+03 | 7.1e-03 7.1e-01 2.8e-02
570 3.9e-01 | 6.4e+04 6.1e+04 | 7.7e+01 1.4e+04 3.0e+03 | 7.0e-03 6.9e-01 2.4e-02
580 4.0e-01 | 6.3e+04 6.1e+04 | 7.5e+01 1.4e+04 2.2e+03 | 6.8e-03 6.8e-01 1.7e-02
590 4.0e-01 | 6.3e+04 6.1e+04 | 7.3e+01 1.3e+04 1.4e+03 | 6.6e-03 6.6e-01 1.2e-02
600 4.1e-01 | 6.2e+04 6.1e+04 | 6.9e+01 1.3e+04 7.9e+02 | 6.3e-03 6.4e-01 6.4e-03
610 4.2e-01 | 6.2e+04 6.1e+04 | 6.8e+01 1.3e+04 4.2e+02 | 6.2e-03 6.3e-01 3.4e-03
620 4.2e-01 | 6.1e+04 6.1e+04 | 6.7e+01 1.3e+04 2.5e+02 | 6.0e-03 6.2e-01 2.1e-03
630 4.3e-01 | 6.0e+04 6.1e+04 | 6.4e+01 1.2e+04 8.7e+02 | 5.8e-03 6.1e-01 7.1e-03
640 4.4e-01 | 6.0e+04 6.1e+04 | 6.3e+01 1.2e+04 1.3e+03 | 5.7e-03 5.9e-01 1.1e-02
650 4.4e-01 | 5.9e+04 6.1e+04 | 6.1e+01 1.2e+04 1.9e+03 | 5.6e-03 5.8e-01 1.6e-02
660 4.5e-01 | 5.9e+04 6.1e+04 | 6.0e+01 1.2e+04 2.3e+03 | 5.5e-03 5.7e-01 1.9e-02
670 4.6e-01 | 5.8e+04 6.1e+04 | 5.9e+01 1.1e+04 2.7e+03 | 5.3e-03 5.6e-01 2.3e-02
680 4.6e-01 | 5.8e+04 6.1e+04 | 5.8e+01 1.1e+04 3.1e+03 | 5.2e-03 5.5e-01 2.6e-02
690 4.7e-01 | 5.7e+04 6.1e+04 | 5.7e+01 1.1e+04 3.4e+03 | 5.1e-03 5.4e-01 2.9e-02
700 4.7e-01 | 5.7e+04 6.1e+04 | 5.6e+01 1.1e+04 3.7e+03 | 5.1e-03 5.3e-01 3.1e-02
710 4.8e-01 | 5.7e+04 6.1e+04 | 5.5e+01 1.0e+04 4.0e+03 | 5.0e-03 5.2e-01 3.4e-02
720 4.9e-01 | 5.6e+04 6.1e+04 | 5.4e+01 1.0e+04 4.3e+03 | 4.9e-03 5.1e-01 3.7e-02
730 4.9e-01 | 5.6e+04 6.0e+04 | 5.3e+01 1.0e+04 4.5e+03 | 4.8e-03 5.0e-01 3.8e-02
740 5.0e-01 | 5.6e+04 6.0e+04 | 5.2e+01 1.0e+04 4.7e+03 | 4.7e-03 4.9e-01 4.0e-02
750 5.1e-01 | 5.5e+04 6.0e+04 | 5.1e+01 9.8e+03 4.9e+03 | 4.6e-03 4.9e-01 4.2e-02
760 5.2e-01 | 5.5e+04 6.0e+04 | 5.1e+01 9.7e+03 5.1e+03 | 4.6e-03 4.8e-01 4.5e-02
770 5.2e-01 | 5.5e+04 6.0e+04 | 4.9e+01 9.5e+03 5.2e+03 | 4.5e-03 4.7e-01 4.6e-02
780 5.3e-01 | 5.4e+04 6.0e+04 | 4.9e+01 9.4e+03 5.5e+03 | 4.4e-03 4.6e-01 4.8e-02
790 5.3e-01 | 5.4e+04 6.0e+04 | 4.9e+01 9.2e+03 5.7e+03 | 4.4e-03 4.6e-01 5.0e-02
800 5.4e-01 | 5.4e+04 6.0e+04 | 4.8e+01 9.1e+03 6.0e+03 | 4.4e-03 4.5e-01 5.3e-02
810 5.5e-01 | 5.3e+04 5.9e+04 | 4.7e+01 8.6e+03 5.1e+03 | 4.2e-03 4.3e-01 4.6e-02
820 5.6e-01 | 5.3e+04 5.8e+04 | 4.6e+01 8.6e+03 4.9e+03 | 4.2e-03 4.2e-01 4.4e-02
830 5.6e-01 | 5.3e+04 5.8e+04 | 4.6e+01 8.5e+03 4.7e+03 | 4.2e-03 4.2e-01 4.3e-02
840 5.7e-01 | 5.3e+04 5.7e+04 | 4.6e+01 8.4e+03 4.7e+03 | 4.1e-03 4.1e-01 4.3e-02
850 5.8e-01 | 5.2e+04 5.7e+04 | 4.6e+01 8.3e+03 4.9e+03 | 4.1e-03 4.1e-01 4.5e-02
860 5.8e-01 | 5.2e+04 5.7e+04 | 4.5e+01 8.2e+03 4.9e+03 | 4.0e-03 4.0e-01 4.5e-02
870 5.9e-01 | 5.2e+04 5.7e+04 | 4.4e+01 8.1e+03 5.0e+03 | 4.0e-03 4.0e-01 4.6e-02
880 6.0e-01 | 5.2e+04 5.7e+04 | 4.3e+01 8.0e+03 4.9e+03 | 3.9e-03 4.0e-01 4.6e-02
890 6.0e-01 | 5.1e+04 5.6e+04 | 4.2e+01 7.9e+03 5.0e+03 | 3.8e-03 3.9e-01 4.7e-02
900 6.1e-01 | 5.1e+04 5.6e+04 | 4.2e+01 7.8e+03 5.1e+03 | 3.8e-03 3.9e-01 4.8e-02
910 6.2e-01 | 5.1e+04 5.6e+04 | 4.1e+01 7.7e+03 5.3e+03 | 3.7e-03 3.8e-01 4.9e-02
920 6.2e-01 | 5.1e+04 5.6e+04 | 4.0e+01 7.6e+03 5.4e+03 | 3.6e-03 3.7e-01 5.1e-02
930 6.3e-01 | 5.0e+04 5.6e+04 | 3.9e+01 7.4e+03 5.6e+03 | 3.5e-03 3.7e-01 5.2e-02
940 6.4e-01 | 5.0e+04 5.6e+04 | 3.8e+01 7.3e+03 5.7e+03 | 3.5e-03 3.6e-01 5.3e-02
950 6.4e-01 | 5.0e+04 5.6e+04 | 3.7e+01 7.2e+03 5.7e+03 | 3.4e-03 3.6e-01 5.4e-02
960 6.5e-01 | 5.0e+04 5.6e+04 | 3.5e+01 7.1e+03 5.8e+03 | 3.2e-03 3.5e-01 5.5e-02
970 6.5e-01 | 5.0e+04 5.6e+04 | 3.5e+01 7.0e+03 5.9e+03 | 3.1e-03 3.4e-01 5.6e-02
980 6.6e-01 | 5.0e+04 5.6e+04 | 3.4e+01 6.9e+03 6.0e+03 | 3.1e-03 3.4e-01 5.7e-02
990 6.7e-01 | 4.9e+04 5.5e+04 | 3.3e+01 6.8e+03 6.1e+03 | 3.0e-03 3.3e-01 5.8e-02
1000 6.8e-01 | 4.9e+04 5.5e+04 | 3.1e+01 6.7e+03 6.1e+03 | 2.8e-03 3.3e-01 5.8e-02
1100 7.3e-01 | 4.8e+04 5.4e+04 | 2.6e+01 5.8e+03 6.4e+03 | 2.4e-03 2.9e-01 6.3e-02
1200 7.9e-01 | 4.7e+04 5.3e+04 | 2.3e+01 5.1e+03 6.4e+03 | 2.1e-03 2.5e-01 6.4e-02
1300 8.4e-01 | 4.6e+04 5.3e+04 | 1.8e+01 4.7e+03 6.3e+03 | 1.6e-03 2.3e-01 6.4e-02
1400 9.0e-01 | 4.6e+04 5.2e+04 | 1.4e+01 4.3e+03 6.2e+03 | 1.3e-03 2.1e-01 6.4e-02
1500 9.6e-01 | 4.5e+04 5.0e+04 | 1.5e+01 3.6e+03 5.3e+03 | 1.4e-03 1.8e-01 5.5e-02
1600 1.0e+00 | 4.5e+04 4.9e+04 | 1.6e+01 3.1e+03 4.9e+03 | 1.5e-03 1.5e-01 5.2e-02
1700 1.1e+00 | 4.4e+04 4.9e+04 | 1.7e+01 2.7e+03 4.7e+03 | 1.5e-03 1.4e-01 5.0e-02
1800 1.1e+00 | 4.4e+04 4.8e+04 | 1.5e+01 2.5e+03 4.4e+03 | 1.4e-03 1.2e-01 4.8e-02
1900 1.2e+00 | 4.4e+04 4.8e+04 | 1.4e+01 2.3e+03 4.2e+03 | 1.2e-03 1.1e-01 4.6e-02
2000 1.2e+00 | 4.3e+04 4.7e+04 | 1.1e+01 2.1e+03 4.0e+03 | 9.9e-04 1.0e-01 4.4e-02
2100 1.3e+00 | 4.3e+04 4.7e+04 | 9.2e+00 1.9e+03 3.8e+03 | 8.3e-04 9.5e-02 4.3e-02
2200 1.4e+00 | 4.3e+04 4.7e+04 | 8.1e+00 1.8e+03 3.6e+03 | 7.3e-04 8.9e-02 4.1e-02
2300 1.4e+00 | 4.3e+04 4.6e+04 | 8.7e+00 1.5e+03 3.0e+03 | 7.9e-04 7.4e-02 3.4e-02
2400 1.5e+00 | 4.2e+04 4.5e+04 | 1.0e+01 1.3e+03 2.7e+03 | 9.2e-04 6.4e-02 3.1e-02
2500 1.5e+00 | 4.2e+04 4.5e+04 | 1.1e+01 1.1e+03 2.5e+03 | 1.0e-03 5.6e-02 2.9e-02
2600 1.6e+00 | 4.2e+04 4.4e+04 | 1.1e+01 1.0e+03 2.3e+03 | 1.0e-03 4.9e-02 2.7e-02
2700 1.6e+00 | 4.2e+04 4.4e+04 | 9.8e+00 8.9e+02 2.2e+03 | 8.9e-04 4.4e-02 2.6e-02
2800 1.7e+00 | 4.2e+04 4.4e+04 | 1.0e+01 8.1e+02 2.1e+03 | 9.2e-04 4.0e-02 2.4e-02
2900 1.8e+00 | 4.2e+04 4.4e+04 | 1.0e+01 7.4e+02 2.0e+03 | 9.4e-04 3.7e-02 2.4e-02
3000 1.8e+00 | 4.2e+04 4.4e+04 | 1.0e+01 6.8e+02 1.9e+03 | 9.2e-04 3.3e-02 2.2e-02
3100 1.9e+00 | 4.2e+04 4.4e+04 | 9.3e+00 6.2e+02 1.9e+03 | 8.4e-04 3.1e-02 2.2e-02
3200 1.9e+00 | 4.2e+04 4.3e+04 | 8.3e+00 5.7e+02 1.8e+03 | 7.5e-04 2.8e-02 2.1e-02
3300 2.0e+00 | 4.2e+04 4.3e+04 | 7.4e+00 5.4e+02 1.7e+03 | 6.7e-04 2.7e-02 2.0e-02
3400 2.0e+00 | 4.2e+04 4.3e+04 | 6.6e+00 5.1e+02 1.7e+03 | 5.9e-04 2.5e-02 2.0e-02
3500 2.1e+00 | 4.2e+04 4.3e+04 | 6.1e+00 4.8e+02 1.6e+03 | 5.5e-04 2.4e-02 1.9e-02
3600 2.2e+00 | 4.2e+04 4.3e+04 | 5.6e+00 4.5e+02 1.6e+03 | 5.1e-04 2.2e-02 1.8e-02
3700 2.2e+00 | 4.1e+04 4.3e+04 | 5.5e+00 3.7e+02 1.2e+03 | 5.0e-04 1.8e-02 1.5e-02
3800 2.3e+00 | 4.1e+04 4.3e+04 | 6.0e+00 3.2e+02 1.1e+03 | 5.5e-04 1.6e-02 1.3e-02
3900 2.3e+00 | 4.1e+04 4.2e+04 | 6.5e+00 2.7e+02 1.0e+03 | 5.9e-04 1.4e-02 1.2e-02
4000 2.4e+00 | 4.1e+04 4.2e+04 | 6.5e+00 2.4e+02 9.6e+02 | 5.8e-04 1.2e-02 1.1e-02
4100 2.4e+00 | 4.1e+04 4.2e+04 | 6.4e+00 2.1e+02 9.2e+02 | 5.8e-04 1.0e-02 1.1e-02
4200 2.5e+00 | 4.1e+04 4.2e+04 | 5.6e+00 1.9e+02 8.7e+02 | 5.1e-04 9.2e-03 1.0e-02
4300 2.6e+00 | 4.1e+04 4.2e+04 | 5.3e+00 1.7e+02 8.4e+02 | 4.8e-04 8.3e-03 1.0e-02
4400 2.6e+00 | 4.1e+04 4.2e+04 | 4.8e+00 1.5e+02 8.2e+02 | 4.4e-04 7.6e-03 9.8e-03
4500 2.7e+00 | 4.1e+04 4.2e+04 | 4.8e+00 1.4e+02 7.8e+02 | 4.3e-04 6.9e-03 9.4e-03
4600 2.7e+00 | 4.1e+04 4.2e+04 | 4.3e+00 1.3e+02 7.6e+02 | 3.8e-04 6.3e-03 9.1e-03
4700 2.8e+00 | 4.1e+04 4.2e+04 | 4.3e+00 1.2e+02 7.4e+02 | 3.8e-04 5.8e-03 8.9e-03
4800 2.8e+00 | 4.1e+04 4.2e+04 | 3.6e+00 1.1e+02 7.2e+02 | 3.3e-04 5.4e-03 8.6e-03
4900 2.9e+00 | 4.1e+04 4.2e+04 | 3.3e+00 1.0e+02 7.0e+02 | 3.0e-04 4.9e-03 8.4e-03
5000 3.0e+00 | 4.1e+04 4.2e+04 | 3.3e+00 9.4e+01 6.9e+02 | 3.0e-04 4.6e-03 8.2e-03
5100 3.0e+00 | 4.1e+04 4.2e+04 | 3.3e+00 8.8e+01 6.6e+02 | 3.0e-04 4.3e-03 7.9e-03
5200 3.1e+00 | 4.1e+04 4.2e+04 | 3.1e+00 8.4e+01 6.5e+02 | 2.8e-04 4.1e-03 7.8e-03
5300 3.1e+00 | 4.1e+04 4.2e+04 | 2.9e+00 7.9e+01 6.5e+02 | 2.6e-04 3.9e-03 7.7e-03
5400 3.2e+00 | 4.1e+04 4.2e+04 | 2.8e+00 7.5e+01 6.3e+02 | 2.5e-04 3.7e-03 7.6e-03
5500 3.2e+00 | 4.1e+04 4.2e+04 | 2.6e+00 7.1e+01 6.2e+02 | 2.4e-04 3.5e-03 7.5e-03
5600 3.3e+00 | 4.1e+04 4.2e+04 | 2.5e+00 6.8e+01 6.1e+02 | 2.3e-04 3.3e-03 7.3e-03
5700 3.4e+00 | 4.1e+04 4.2e+04 | 2.5e+00 5.3e+01 5.5e+02 | 2.3e-04 2.6e-03 6.6e-03
5800 3.4e+00 | 4.1e+04 4.2e+04 | 2.4e+00 4.7e+01 5.3e+02 | 2.2e-04 2.3e-03 6.3e-03
5900 3.5e+00 | 4.1e+04 4.2e+04 | 2.4e+00 4.2e+01 5.1e+02 | 2.1e-04 2.1e-03 6.1e-03
6000 3.5e+00 | 4.1e+04 4.2e+04 | 2.3e+00 3.8e+01 5.0e+02 | 2.1e-04 1.9e-03 6.0e-03
6100 3.6e+00 | 4.1e+04 4.2e+04 | 2.2e+00 3.4e+01 4.9e+02 | 2.0e-04 1.7e-03 5.9e-03
6200 3.6e+00 | 4.1e+04 4.2e+04 | 2.1e+00 3.1e+01 4.8e+02 | 1.9e-04 1.5e-03 5.8e-03
6300 3.7e+00 | 4.1e+04 4.2e+04 | 2.1e+00 2.9e+01 4.8e+02 | 1.9e-04 1.4e-03 5.7e-03
6400 3.8e+00 | 4.1e+04 4.2e+04 | 2.0e+00 2.7e+01 4.7e+02 | 1.8e-04 1.3e-03 5.7e-03
6500 3.8e+00 | 4.1e+04 4.2e+04 | 2.0e+00 2.5e+01 4.7e+02 | 1.8e-04 1.3e-03 5.6e-03
6600 3.9e+00 | 4.1e+04 4.2e+04 | 2.0e+00 2.4e+01 4.6e+02 | 1.8e-04 1.2e-03 5.5e-03
6700 3.9e+00 | 4.1e+04 4.2e+04 | 1.9e+00 2.2e+01 4.6e+02 | 1.7e-04 1.1e-03 5.5e-03
6800 4.0e+00 | 4.1e+04 4.2e+04 | 1.9e+00 2.1e+01 4.6e+02 | 1.7e-04 1.0e-03 5.5e-03
6900 4.0e+00 | 4.1e+04 4.2e+04 | 1.8e+00 1.9e+01 4.6e+02 | 1.6e-04 9.6e-04 5.5e-03
7000 4.1e+00 | 4.1e+04 4.2e+04 | 1.7e+00 1.9e+01 4.5e+02 | 1.5e-04 9.2e-04 5.4e-03
7100 4.2e+00 | 4.1e+04 4.2e+04 | 1.7e+00 1.8e+01 4.5e+02 | 1.5e-04 8.8e-04 5.4e-03
7200 4.2e+00 | 4.1e+04 4.2e+04 | 1.6e+00 1.7e+01 4.4e+02 | 1.4e-04 8.4e-04 5.3e-03
7300 4.3e+00 | 4.1e+04 4.2e+04 | 1.5e+00 1.6e+01 4.4e+02 | 1.4e-04 8.0e-04 5.3e-03
7400 4.3e+00 | 4.1e+04 4.2e+04 | 1.5e+00 1.6e+01 4.4e+02 | 1.4e-04 7.8e-04 5.3e-03
7500 4.4e+00 | 4.1e+04 4.2e+04 | 1.5e+00 1.5e+01 4.4e+02 | 1.4e-04 7.4e-04 5.3e-03
7600 4.4e+00 | 4.1e+04 4.2e+04 | 1.5e+00 1.5e+01 4.4e+02 | 1.3e-04 7.2e-04 5.2e-03
7700 4.5e+00 | 4.2e+04 4.2e+04 | 1.5e+00 1.4e+01 4.3e+02 | 1.3e-04 6.9e-04 5.2e-03
7800 4.6e+00 | 4.2e+04 4.2e+04 | 1.4e+00 1.4e+01 4.3e+02 | 1.3e-04 6.8e-04 5.2e-03
7900 4.6e+00 | 4.2e+04 4.2e+04 | 1.4e+00 1.3e+01 4.3e+02 | 1.3e-04 6.5e-04 5.2e-03
8000 4.7e+00 | 4.2e+04 4.2e+04 | 1.4e+00 1.3e+01 4.3e+02 | 1.3e-04 6.3e-04 5.1e-03
8100 4.7e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.3e+01 4.3e+02 | 1.2e-04 6.2e-04 5.1e-03
8200 4.8e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.2e+01 4.2e+02 | 1.2e-04 6.1e-04 5.1e-03
8300 4.8e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.2e+01 4.2e+02 | 1.2e-04 5.9e-04 5.0e-03
8400 4.9e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.2e+01 4.2e+02 | 1.2e-04 5.8e-04 5.0e-03
8500 5.0e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.1e+01 4.2e+02 | 1.2e-04 5.6e-04 5.0e-03
8600 5.0e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.1e+01 4.2e+02 | 1.2e-04 5.4e-04 5.0e-03
8700 5.1e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.1e+01 4.2e+02 | 1.2e-04 5.2e-04 5.0e-03
8800 5.1e+00 | 4.2e+04 4.2e+04 | 1.3e+00 1.0e+01 4.1e+02 | 1.1e-04 5.1e-04 5.0e-03
8900 5.2e+00 | 4.2e+04 4.2e+04 | 1.2e+00 1.1e+01 4.1e+02 | 1.1e-04 5.6e-04 4.9e-03
9000 5.2e+00 | 4.2e+04 4.2e+04 | 1.2e+00 1.2e+01 4.1e+02 | 1.1e-04 5.9e-04 4.9e-03
9100 5.3e+00 | 4.2e+04 4.2e+04 | 1.2e+00 1.2e+01 4.1e+02 | 1.1e-04 6.1e-04 4.9e-03
9200 5.4e+00 | 4.2e+04 4.2e+04 | 1.2e+00 1.3e+01 4.1e+02 | 1.1e-04 6.3e-04 4.9e-03
9300 5.4e+00 | 4.2e+04 4.2e+04 | 1.2e+00 1.3e+01 4.1e+02 | 1.1e-04 6.5e-04 4.9e-03
9400 5.5e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.4e+01 4.1e+02 | 1.0e-04 6.7e-04 4.9e-03
9500 5.5e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.4e+01 4.1e+02 | 1.0e-04 6.9e-04 4.9e-03
9600 5.6e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.4e+01 4.1e+02 | 1.0e-04 7.1e-04 4.9e-03
9700 5.6e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.5e+01 4.0e+02 | 1.0e-04 7.2e-04 4.8e-03
9800 5.7e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.5e+01 4.0e+02 | 9.9e-05 7.3e-04 4.8e-03
9900 5.8e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.5e+01 4.0e+02 | 9.8e-05 7.4e-04 4.8e-03
10000 5.8e+00 | 4.2e+04 4.2e+04 | 1.1e+00 1.5e+01 4.0e+02 | 9.6e-05 7.5e-04 4.8e-03
11000 6.4e+00 | 4.2e+04 4.2e+04 | 9.6e-01 1.7e+01 3.8e+02 | 8.7e-05 8.4e-04 4.6e-03
12000 6.9e+00 | 4.2e+04 4.2e+04 | 8.2e-01 1.7e+01 3.5e+02 | 7.4e-05 8.5e-04 4.2e-03
13000 7.5e+00 | 4.2e+04 4.2e+04 | 7.4e-01 1.6e+01 3.2e+02 | 6.7e-05 8.0e-04 3.9e-03
14000 8.0e+00 | 4.2e+04 4.2e+04 | 6.5e-01 2.2e+01 3.0e+02 | 5.9e-05 1.1e-03 3.6e-03
15000 8.5e+00 | 4.2e+04 4.2e+04 | 5.6e-01 4.0e+01 2.7e+02 | 5.1e-05 2.0e-03 3.2e-03
16000 9.1e+00 | 4.2e+04 4.2e+04 | 4.9e-01 5.0e+01 1.9e+02 | 4.4e-05 2.5e-03 2.3e-03
17000 9.6e+00 | 4.2e+04 4.2e+04 | 3.8e-01 4.5e+01 1.0e+02 | 3.5e-05 2.2e-03 1.2e-03
18000 1.0e+01 | 4.2e+04 4.2e+04 | 2.2e-01 3.5e+01 6.5e+01 | 2.0e-05 1.7e-03 7.7e-04
19000 1.1e+01 | 4.2e+04 4.2e+04 | 1.7e-01 2.9e+01 4.7e+01 | 1.5e-05 1.4e-03 5.6e-04
20000 1.1e+01 | 4.2e+04 4.2e+04 | 1.3e-01 2.4e+01 4.2e+01 | 1.2e-05 1.2e-03 5.0e-04
21000 1.2e+01 | 4.2e+04 4.2e+04 | 1.2e-01 2.1e+01 3.9e+01 | 1.1e-05 1.0e-03 4.6e-04
22000 1.2e+01 | 4.2e+04 4.2e+04 | 1.1e-01 1.6e+01 2.7e+01 | 1.0e-05 8.0e-04 3.2e-04
23000 1.3e+01 | 4.2e+04 4.2e+04 | 9.5e-02 1.4e+01 1.2e+01 | 8.6e-06 7.1e-04 1.5e-04
24000 1.4e+01 | 4.2e+04 4.2e+04 | 7.6e-02 1.3e+01 9.2e-01 | 6.9e-06 6.2e-04 1.1e-05
25000 1.4e+01 | 4.2e+04 4.2e+04 | 5.8e-02 1.0e+01 4.2e+00 | 5.2e-06 5.2e-04 5.0e-05
26000 1.5e+01 | 4.2e+04 4.2e+04 | 4.8e-02 9.0e+00 5.7e+00 | 4.4e-06 4.4e-04 6.8e-05
27000 1.5e+01 | 4.2e+04 4.2e+04 | 4.0e-02 7.8e+00 5.0e+00 | 3.6e-06 3.9e-04 6.0e-05
28000 1.6e+01 | 4.2e+04 4.2e+04 | 3.3e-02 7.1e+00 3.9e+00 | 3.0e-06 3.5e-04 4.6e-05
29000 1.6e+01 | 4.2e+04 4.2e+04 | 3.2e-02 6.5e+00 2.7e+00 | 2.9e-06 3.2e-04 3.2e-05
30000 1.7e+01 | 4.2e+04 4.2e+04 | 2.9e-02 5.8e+00 1.9e+00 | 2.6e-06 2.9e-04 2.2e-05
31000 1.7e+01 | 4.2e+04 4.2e+04 | 2.9e-02 5.4e+00 1.7e+00 | 2.6e-06 2.7e-04 2.1e-05
32000 1.8e+01 | 4.2e+04 4.2e+04 | 2.8e-02 4.9e+00 1.6e+00 | 2.5e-06 2.4e-04 1.9e-05
33000 1.8e+01 | 4.2e+04 4.2e+04 | 2.8e-02 4.6e+00 1.5e+00 | 2.6e-06 2.3e-04 1.8e-05
34000 1.9e+01 | 4.2e+04 4.2e+04 | 4.0e-02 4.1e+00 3.1e+00 | 3.6e-06 2.0e-04 3.7e-05
35000 2.0e+01 | 4.2e+04 4.2e+04 | 7.9e-02 3.0e+00 7.0e+00 | 7.1e-06 1.5e-04 8.4e-05
36000 2.0e+01 | 4.2e+04 4.2e+04 | 7.6e-02 2.4e+00 8.6e+00 | 6.8e-06 1.2e-04 1.0e-04
37000 2.1e+01 | 4.2e+04 4.2e+04 | 6.7e-02 1.9e+00 9.1e+00 | 6.1e-06 9.2e-05 1.1e-04
38000 2.1e+01 | 4.2e+04 4.2e+04 | 6.4e-02 1.5e+00 8.4e+00 | 5.7e-06 7.6e-05 1.0e-04
39000 2.2e+01 | 4.2e+04 4.2e+04 | 6.1e-02 1.3e+00 8.0e+00 | 5.5e-06 6.2e-05 9.5e-05
40000 2.2e+01 | 4.2e+04 4.2e+04 | 5.7e-02 1.1e+00 7.8e+00 | 5.1e-06 5.3e-05 9.2e-05
41000 2.3e+01 | 4.2e+04 4.2e+04 | 5.3e-02 9.3e-01 7.3e+00 | 4.8e-06 4.6e-05 8.7e-05
42000 2.3e+01 | 4.2e+04 4.2e+04 | 4.8e-02 8.4e-01 6.6e+00 | 4.3e-06 4.2e-05 7.9e-05
43000 2.4e+01 | 4.2e+04 4.2e+04 | 4.1e-02 7.7e-01 6.1e+00 | 3.7e-06 3.8e-05 7.2e-05
44000 2.5e+01 | 4.2e+04 4.2e+04 | 3.8e-02 7.0e-01 5.6e+00 | 3.4e-06 3.5e-05 6.6e-05
45000 2.5e+01 | 4.2e+04 4.2e+04 | 3.2e-02 6.5e-01 5.2e+00 | 2.9e-06 3.2e-05 6.3e-05
46000 2.6e+01 | 4.2e+04 4.2e+04 | 2.8e-02 6.2e-01 4.6e+00 | 2.5e-06 3.1e-05 5.5e-05
47000 2.6e+01 | 4.2e+04 4.2e+04 | 2.9e-02 5.2e-01 4.3e+00 | 2.6e-06 2.6e-05 5.1e-05
48000 2.7e+01 | 4.2e+04 4.2e+04 | 2.6e-02 4.7e-01 3.8e+00 | 2.4e-06 2.3e-05 4.5e-05
49000 2.7e+01 | 4.2e+04 4.2e+04 | 2.5e-02 4.3e-01 3.2e+00 | 2.3e-06 2.1e-05 3.9e-05
50000 2.8e+01 | 4.2e+04 4.2e+04 | 2.5e-02 3.9e-01 2.8e+00 | 2.2e-06 1.9e-05 3.3e-05
51000 2.8e+01 | 4.2e+04 4.2e+04 | 2.3e-02 3.7e-01 2.3e+00 | 2.1e-06 1.8e-05 2.8e-05
52000 2.9e+01 | 4.2e+04 4.2e+04 | 2.1e-02 3.5e-01 1.9e+00 | 1.9e-06 1.7e-05 2.3e-05
53000 3.0e+01 | 4.2e+04 4.2e+04 | 1.9e-02 3.3e-01 1.5e+00 | 1.7e-06 1.6e-05 1.8e-05
54000 3.0e+01 | 4.2e+04 4.2e+04 | 1.7e-02 3.1e-01 1.1e+00 | 1.5e-06 1.5e-05 1.3e-05
55000 3.1e+01 | 4.2e+04 4.2e+04 | 1.5e-02 3.0e-01 8.0e-01 | 1.3e-06 1.5e-05 9.5e-06
56000 3.1e+01 | 4.2e+04 4.2e+04 | 1.3e-02 2.8e-01 5.4e-01 | 1.1e-06 1.4e-05 6.4e-06
57000 3.2e+01 | 4.2e+04 4.2e+04 | 1.1e-02 2.5e-01 3.2e-01 | 1.0e-06 1.3e-05 3.8e-06
58000 3.2e+01 | 4.2e+04 4.2e+04 | 9.5e-03 2.3e-01 2.2e-01 | 8.6e-07 1.1e-05 2.7e-06
59000 3.3e+01 | 4.2e+04 4.2e+04 | 9.5e-03 2.2e-01 1.9e-01 | 8.6e-07 1.1e-05 2.2e-06
60000 3.3e+01 | 4.2e+04 4.2e+04 | 9.8e-03 2.0e-01 1.4e-01 | 8.9e-07 9.8e-06 1.6e-06
---------------------------------------------------------------------------------------
Solution Summary
Status : OPTIMAL
Iterations : 60600
Solve time : 33.7 sec
Primal obj : 41950.94959
Dual obj : 41950.8804
Primal infeas : 8.759e-07
Dual infeas : 9.163e-06
@PC:~/cuPDLPx-main/cuPDLPx-main/build$