COPTに対して、Cuoptを評価しました。インスタンスは、instance24ですが、LB値を求める途中のものを使用しています。
下記に結果を示しますが、評価環境が違うことに注意してください。COPTの評価環境は、CPU/GPU共Cuoptの評価環境のおよそ倍以上の性能が違います。Cuopt、BarrierGPUでは、インスタンス23でも数値エラーとなっていました。インスタンス22では、計測できましたが、PDLPに比べかなり遅い結果となっており、仮に数値演算エラーが無くなったとしても期待できない、と考えます。ちなみにBarrierSolverは、Cutoptに限らず、数値演算エラーが生じ易いようで、数値演算エラーが出たときの救済策は考えておく必要があります。
＜COPT PDLPとCOPT PDLPの差＞
恐らくは、COPTが未だPDLPXを実装していない、のが原因と思われます。ライセンス評価期間内に実装されることを望みます。（サポートと話をする機会があれば、聞いてみたいと思います。）
GPUの性能が約3.7倍であることを考慮すると、Cuopt PDLPは､COPT Barrierよりも高速という結論になります。
Cuoptは､DOCKERで計算サーバを立ち上げることもサポートしているので、Windowsの実装のままWSL2上にローカルサーバを構築し、REST APIでLP計算を依頼する実装も可能です。また、それとは別に、PDLPXは、C++実装が公開され、WarmStartもサポートしています。（Branch操作において、WarmStartは必須です。）これをC++の開発中ソルバに組み込むことも可能です。COPTのREST APIを実装する手間と、C++組み込みの手間とどちらがよいか悩みところですが、PDLPX化の課題は、それだけではなく、実務的には、crossoverを実装する必要があります。幸い同じ著者による実装が公開されていますが、この辺のところまでコントロールするなると結構大変です。全てが揃っているCOPTがやってくれれば、余計なことに悩む必要はありません。
COPT> set lpmethod 2
Setting parameter 'LpMethod' to 2
COPT> set crossover 0
Setting parameter 'Crossover' to 0
COPT> read instance24.lp
Reading from 'C:\Users\.PC\highs_test\instance24.lp'
Reading finished (0.62s)
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
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [6e-02,5e+01]
Range of rhs coefficients: [4e-01,7e+01]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,4e+04]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 6.485e+07
Number of factor entries: 7.216e+07
Number of factor flops: 5.209e+11
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +6.89041521e+07 -1.47285422e+08 5.11e+08 2.93e+03 3.86e+04 20.29s
1 +2.06731774e+07 -4.05798355e+07 7.96e+07 2.95e+02 4.35e+03 23.00s
2 +1.51129327e+06 -2.46845951e+06 4.38e+06 1.09e+01 1.98e+02 25.97s
3 +2.34855347e+05 -3.81229124e+05 6.46e+05 1.21e+00 2.72e+01 28.98s
4 +9.01673726e+04 -6.33129847e+04 1.57e+05 2.42e-01 5.99e+00 31.98s
5 +6.76374779e+04 -8.77178644e+03 7.77e+04 1.24e-01 2.80e+00 34.96s
6 +5.47063786e+04 +2.14338969e+04 3.37e+04 5.75e-02 1.08e+00 37.73s
7 +5.11497402e+04 +2.99006339e+04 2.15e+04 4.20e-02 6.24e-01 40.31s
8 +4.69504087e+04 +3.57171024e+04 1.13e+04 2.28e-02 3.05e-01 43.07s
9 +4.48897023e+04 +3.80587025e+04 6.88e+03 1.38e-02 1.85e-01 45.68s
10 +4.45573602e+04 +3.88240627e+04 5.77e+03 1.23e-02 1.48e-01 48.20s
11 +4.31919111e+04 +4.03641692e+04 2.84e+03 5.75e-03 7.25e-02 50.90s
12 +4.25249991e+04 +4.13820700e+04 1.15e+03 2.52e-03 2.42e-02 53.93s
13 +4.21968343e+04 +4.16899379e+04 5.09e+02 1.06e-03 1.03e-02 56.74s
14 +4.20201086e+04 +4.18738306e+04 1.47e+02 2.80e-04 2.79e-03 59.76s
15 +4.19956492e+04 +4.19029428e+04 9.30e+01 1.81e-04 1.73e-03 62.30s
16 +4.19603624e+04 +4.19413862e+04 1.90e+01 3.60e-05 3.04e-04 65.31s
17 +4.19527894e+04 +4.19491700e+04 3.63e+00 7.10e-06 4.88e-05 68.31s
18 +4.19519892e+04 +4.19499133e+04 2.08e+00 4.18e-06 2.72e-05 70.81s
19 +4.19510585e+04 +4.19506456e+04 4.14e-01 7.27e-07 5.90e-06 73.72s
20 +4.19508865e+04 +4.19508330e+04 5.36e-02 8.65e-08 7.75e-07 76.74s
21 +4.19508736e+04 +4.19508441e+04 2.96e-02 4.07e-08 4.80e-07 79.34s
22 +4.19508687e+04 +4.19508558e+04 1.29e-02 2.31e-08 1.68e-07 81.92s
23 +4.19508649e+04 +4.19508586e+04 6.33e-03 1.10e-08 8.93e-08 84.48s
24 +4.19508620e+04 +4.19508616e+04 4.04e-04 6.78e-09 6.45e-09 87.32s
Barrier status: OPTIMAL
Primal objective: 4.19508620e+04
Dual objective: 4.19508616e+04
Duality gap (abs/rel): 4.03e-04 / 9.61e-09
Primal infeasibility (abs/rel): 6.78e-09 / 7.53e-10
Dual infeasibility (abs/rel): 6.45e-09 / 1.68e-13
Postsolving
Solving finished
Status: Optimal Objective: 4.1950862012e+04 Iterations: 24(0) Time: 87.50s
COPT> set gpumode 1
Setting parameter 'GPUMode' to 1
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 barrier solver using 8 CPU threads and GPU 0
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [6e-02,5e+01]
Range of rhs coefficients: [4e-01,7e+01]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,4e+04]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 6.485e+07
Number of factor entries: 7.216e+07
Number of factor flops: 5.209e+11
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +6.89041521e+07 -1.47285422e+08 5.11e+08 2.93e+03 3.86e+04 20.43s
1 +2.06731774e+07 -4.05798355e+07 7.96e+07 2.95e+02 4.35e+03 22.78s
2 +1.51129327e+06 -2.46845951e+06 4.38e+06 1.09e+01 1.98e+02 25.28s
3 +2.08981694e+05 -3.21353877e+05 5.55e+05 1.01e+00 2.23e+01 27.87s
4 +1.50797642e+05 -1.91581467e+05 3.55e+05 6.55e-01 1.43e+01 30.14s
5 +7.69542411e+04 -3.84123392e+04 1.18e+05 1.86e-01 4.59e+00 32.55s
6 +5.72886861e+04 +1.30200724e+04 4.49e+04 7.17e-02 1.59e+00 34.95s
7 +5.28199307e+04 +2.48832838e+04 2.83e+04 5.10e-02 9.35e-01 37.21s
8 +4.93139363e+04 +3.14684082e+04 1.80e+04 3.57e-02 5.57e-01 39.46s
9 +4.64869445e+04 +3.53299716e+04 1.13e+04 2.24e-02 3.45e-01 41.75s
10 +4.49554866e+04 +3.72739519e+04 7.74e+03 1.51e-02 2.41e-01 44.03s
11 +4.42270257e+04 +3.85967370e+04 5.67e+03 1.13e-02 1.74e-01 46.28s
12 +4.34448741e+04 +3.97930041e+04 3.67e+03 7.37e-03 1.12e-01 48.55s
13 +4.31180677e+04 +4.02015265e+04 2.93e+03 5.75e-03 9.12e-02 50.78s
14 +4.25586573e+04 +4.10818743e+04 1.48e+03 2.85e-03 4.42e-02 53.20s
15 +4.24566883e+04 +4.13332744e+04 1.13e+03 2.36e-03 3.17e-02 55.43s
16 +4.21090974e+04 +4.17650782e+04 3.45e+02 7.22e-04 8.69e-03 58.03s
17 +4.20776772e+04 +4.18154490e+04 2.63e+02 5.81e-04 6.30e-03 60.29s
18 +4.20175668e+04 +4.18758590e+04 1.42e+02 3.05e-04 3.40e-03 62.64s
19 +4.19982883e+04 +4.18983411e+04 1.00e+02 2.16e-04 2.39e-03 64.88s
20 +4.19592054e+04 +4.19397701e+04 1.95e+01 3.48e-05 4.62e-04 67.39s
21 +4.19527727e+04 +4.19480929e+04 4.69e+00 7.30e-06 1.13e-04 69.84s
22 +4.19511738e+04 +4.19504306e+04 7.45e-01 1.06e-06 1.75e-05 72.33s
23 +4.19510182e+04 +4.19506430e+04 3.76e-01 5.26e-07 8.95e-06 74.61s
24 +4.19508776e+04 +4.19508442e+04 3.35e-02 4.36e-08 7.53e-07 77.14s
25 +4.19508632e+04 +4.19508604e+04 2.87e-03 1.74e-08 6.06e-08 79.71s
26 +4.19508622e+04 +4.19508614e+04 8.25e-04 3.16e-08 1.97e-08 82.09s
27 +4.19508619e+04 +4.19508615e+04 4.11e-04 2.53e-08 1.29e-08 84.39s
Barrier status: OPTIMAL
Primal objective: 4.19508619e+04
Dual objective: 4.19508615e+04
Duality gap (abs/rel): 4.15e-04 / 9.90e-09
Primal infeasibility (abs/rel): 2.53e-08 / 2.81e-09
Dual infeasibility (abs/rel): 1.29e-08 / 3.37e-13
Postsolving
Solving finished
Status: Optimal Objective: 4.1950861950e+04 Iterations: 27(0) Time: 84.64s
COPT> set lpmethod 6
Setting parameter 'LpMethod' to 6
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 4.15s
4000 +4.17407991e+04 +3.04897437e+04 +1.13e+04 2.98e+00 3.50e-01 6.63s
8000 +4.19070214e+04 +4.08247925e+04 +1.08e+03 1.13e+00 3.70e-02 8.82s
12000 +4.19414758e+04 +4.16358914e+04 +3.06e+02 4.70e-01 1.04e-02 11.00s
16000 +4.19482878e+04 +4.18529461e+04 +9.53e+01 1.90e-01 3.07e-03 13.17s
20000 +4.19509475e+04 +4.18808838e+04 +7.01e+01 1.31e-01 2.14e-03 15.36s
24000 +4.19503849e+04 +4.18968156e+04 +5.36e+01 8.06e-02 1.69e-03 17.55s
28000 +4.19513357e+04 +4.19022223e+04 +4.91e+01 6.54e-02 1.52e-03 19.72s
32000 +4.19500141e+04 +4.19077636e+04 +4.23e+01 5.78e-02 1.34e-03 21.93s
36000 +4.19503340e+04 +4.18930356e+04 +5.73e+01 4.79e-02 1.88e-03 24.13s
40000 +4.19512214e+04 +4.18980661e+04 +5.32e+01 4.64e-02 1.95e-03 26.32s
44000 +4.19517251e+04 +4.19044864e+04 +4.72e+01 4.24e-02 1.47e-03 28.51s
48000 +4.19519873e+04 +4.19109102e+04 +4.11e+01 3.67e-02 1.31e-03 30.71s
52000 +4.19507950e+04 +4.18687117e+04 +8.21e+01 4.05e-02 2.65e-03 32.93s
56000 +4.19510083e+04 +4.18951665e+04 +5.58e+01 3.67e-02 3.33e-01 35.14s
60000 +4.19508867e+04 +4.19031857e+04 +4.77e+01 2.64e-02 1.52e-03 37.36s
64000 +4.19502261e+04 +4.19103260e+04 +3.99e+01 2.44e-02 1.25e-03 39.58s
68000 +4.19505520e+04 +4.19165477e+04 +3.40e+01 2.03e-02 1.08e-03 41.80s
72000 +4.19510967e+04 +4.19211335e+04 +3.00e+01 2.19e-02 9.25e-04 44.01s
76000 +4.19509285e+04 +4.19249344e+04 +2.60e+01 1.64e-02 7.93e-04 46.22s
80000 +4.19510760e+04 +4.19055577e+04 +4.55e+01 2.56e-02 1.48e-03 48.45s
84000 +4.19506571e+04 +4.19217738e+04 +2.89e+01 1.92e-02 8.98e-04 50.66s
88000 +4.19508379e+04 +4.19269419e+04 +2.39e+01 1.67e-02 7.64e-04 52.87s
92000 +4.19508950e+04 +4.19301711e+04 +2.07e+01 1.52e-02 6.42e-04 55.08s
96000 +4.19509516e+04 +4.19322505e+04 +1.87e+01 1.42e-02 5.79e-04 57.31s
100000 +4.19510837e+04 +4.19340930e+04 +1.70e+01 1.26e-02 5.27e-04 59.51s
104000 +4.19508114e+04 +4.19355736e+04 +1.52e+01 1.19e-02 4.77e-04 61.73s
108000 +4.19508323e+04 +4.19366070e+04 +1.42e+01 1.02e-02 4.35e-04 63.95s
112000 +4.19507764e+04 +4.19381225e+04 +1.27e+01 9.66e-03 4.19e-04 66.17s
116000 +4.19510914e+04 +4.19389582e+04 +1.21e+01 1.01e-02 3.63e-04 68.39s
120000 +4.19509229e+04 +4.19401513e+04 +1.08e+01 9.40e-03 3.40e-04 70.60s
124000 +4.19508567e+04 +4.19402380e+04 +1.06e+01 7.96e-03 3.75e-04 72.82s
128000 +4.19508746e+04 +4.19446876e+04 +6.19e+00 6.75e-03 1.96e-04 75.05s
132000 +4.19507884e+04 +4.19456953e+04 +5.09e+00 6.51e-03 1.61e-04 77.28s
136000 +4.19508935e+04 +4.19462747e+04 +4.62e+00 6.52e-03 1.41e-04 79.51s
140000 +4.19508247e+04 +4.19466312e+04 +4.19e+00 6.01e-03 1.29e-04 81.72s
144000 +4.19507159e+04 +4.19470167e+04 +3.70e+00 6.23e-03 1.21e-04 83.96s
148000 +4.19508886e+04 +4.19471295e+04 +3.76e+00 4.95e-03 1.14e-04 86.19s
152000 +4.19508882e+04 +4.19474299e+04 +3.46e+00 5.94e-03 1.06e-04 88.43s
156000 +4.19507225e+04 +4.19474303e+04 +3.29e+00 4.48e-03 1.11e-04 90.66s
160000 +4.19508571e+04 +4.19476056e+04 +3.25e+00 5.01e-03 9.95e-05 92.89s
164000 +4.19509950e+04 +4.19476968e+04 +3.30e+00 4.79e-03 1.00e-04 95.13s
168000 +4.19509529e+04 +4.19478663e+04 +3.09e+00 4.70e-03 9.31e-05 97.35s
172000 +4.19508620e+04 +4.19479273e+04 +2.93e+00 3.99e-03 9.24e-05 99.58s
176000 +4.19507600e+04 +4.19480613e+04 +2.70e+00 4.59e-03 7.03e-03 101s
180000 +4.19509239e+04 +4.19481562e+04 +2.77e+00 4.17e-03 8.41e-05 104s
184000 +4.19508979e+04 +4.19482315e+04 +2.67e+00 3.92e-03 8.42e-05 106s
188000 +4.19508813e+04 +4.19483136e+04 +2.57e+00 4.21e-03 1.13e-04 108s
192000 +4.19508572e+04 +4.19487905e+04 +2.07e+00 2.65e-03 7.23e-05 110s
196000 +4.19508643e+04 +4.19493215e+04 +1.54e+00 2.82e-03 4.93e-05 112s
200000 +4.19508545e+04 +4.19494812e+04 +1.37e+00 2.43e-03 4.27e-05 115s
204000 +4.19508242e+04 +4.19496231e+04 +1.20e+00 2.41e-03 3.84e-05 117s
208000 +4.19508278e+04 +4.19497299e+04 +1.10e+00 2.33e-03 3.53e-05 119s
212000 +4.19508570e+04 +4.19497641e+04 +1.09e+00 2.14e-03 3.43e-05 121s
216000 +4.19508813e+04 +4.19498278e+04 +1.05e+00 2.27e-03 3.17e-05 124s
220000 +4.19508783e+04 +4.19498143e+04 +1.06e+00 2.03e-03 6.76e-05 126s
224000 +4.19509001e+04 +4.19499121e+04 +9.88e-01 2.38e-03 2.90e-05 128s
228000 +4.19508655e+04 +4.19499468e+04 +9.19e-01 2.06e-03 2.88e-05 130s
232000 +4.19508844e+04 +4.19499751e+04 +9.09e-01 2.24e-03 2.73e-05 133s
236000 +4.19508559e+04 +4.19499898e+04 +8.66e-01 2.06e-03 2.74e-05 135s
240000 +4.19508181e+04 +4.19500076e+04 +8.10e-01 1.79e-03 2.68e-05 137s
244000 +4.19507979e+04 +4.19500302e+04 +7.68e-01 2.04e-03 2.58e-05 139s
248000 +4.19508312e+04 +4.19500505e+04 +7.81e-01 1.80e-03 2.54e-05 142s
252000 +4.19508430e+04 +4.19500623e+04 +7.81e-01 1.68e-03 2.52e-05 144s
256000 +4.19508648e+04 +4.19500766e+04 +7.88e-01 1.54e-03 2.44e-05 146s
260000 +4.19508884e+04 +4.19500939e+04 +7.94e-01 1.87e-03 3.94e-05 148s
264000 +4.19508957e+04 +4.19500869e+04 +8.09e-01 1.65e-03 2.38e-05 150s
268000 +4.19508912e+04 +4.19501136e+04 +7.78e-01 1.64e-03 2.36e-05 153s
272000 +4.19508724e+04 +4.19501426e+04 +7.30e-01 1.68e-03 2.28e-05 155s
276000 +4.19508528e+04 +4.19499680e+04 +8.85e-01 1.60e-03 2.97e-05 157s
280000 +4.19508641e+04 +4.19502685e+04 +5.96e-01 1.23e-03 1.88e-05 159s
284000 +4.19508608e+04 +4.19503494e+04 +5.11e-01 1.08e-03 1.58e-05 162s
288000 +4.19508616e+04 +4.19504107e+04 +4.51e-01 1.20e-03 1.39e-05 164s
292000 +4.19508758e+04 +4.19504364e+04 +4.39e-01 1.08e-03 1.34e-05 166s
293600 +4.19508627e+04 +4.19507789e+04 +8.38e-02 3.67e-04 2.53e-06 167s
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: 167.63s
(.venv) root@dev1:/home/# cuopt_cli --method=1 --presolve=true --relative-primal-tolerance=1e-6 test/instance24.mps
Setting parameter method to 1
Setting parameter presolve to true
Setting parameter relative_primal_tolerance to 1.000000e-06
Reading file instance24.mps
cuOpt version: 25.10.1, git hash: 876fcfc, host arch: x86_64, device archs: 75-real,80-real,86-real,90a-real,100f-real,120a-real,120
CPU: AMD Ryzen 5 2600 Six-Core Processor, threads (physical/logical): 6/12, RAM: 5.71 GiB
CUDA 13.0, device: NVIDIA GeForce GTX 1660 (ID 0), VRAM: 6.00 GiB
CUDA device UUID: ffffff9bffffffbcffffffa225-ffffffa72
Solving a problem with 14135 constraints, 84693 variables (0 integers), and 11800327 nonzeros
Problem scaling:
Objective coefficents range: [1e+00, 3e+02]
Constraint matrix coefficients range: [1e+00, 3e+03]
Constraint rhs / bounds range: [1e+00, 1e+03]
Variable bounds range: [0e+00, 1e+02]
Original problem: 14135 constraints, 84693 variables, 11800327 nonzeros
Calling Papilo presolver
Disabling the presolver methods that do not support dual postsolve
Presolve status: reduced the problem
Presolve removed: 1027 constraints, 13985 variables, 269128 nonzeros
Presolved problem: 13108 constraints, 70708 variables, 11531199 nonzeros
Papilo presolve time: 4.054019
Objective offset 42112200.000000 scaling_factor 1.000000
Iter Primal Obj. Dual Obj. Gap Primal Res. Dual Res. Time
0 +4.21122000e+07 +4.21122000e+07 0.00e+00 1.22e+01 7.36e+07 4.211s
1000 +7.10231166e+04 +8.87823939e+04 1.78e+04 1.42e+01 2.36e+04 6.327s
2000 +8.22431388e+04 +5.63061842e+04 2.59e+04 1.64e+00 5.21e+03 8.163s
3000 +8.14735222e+04 +4.57217637e+04 3.58e+04 1.28e+00 1.37e+03 10.001s
4000 +5.85322830e+04 +4.30805984e+04 1.55e+04 2.28e+00 5.00e+02 11.839s
5000 +5.18175772e+04 +4.24257375e+04 9.39e+03 1.16e+00 2.30e+02 13.674s
6000 +4.45638298e+04 +4.20909159e+04 2.47e+03 1.38e+00 1.10e+02 15.509s
7000 +4.40521924e+04 +4.19842329e+04 2.07e+03 1.21e+00 4.65e+01 17.346s
8000 +4.40021685e+04 +4.19670984e+04 2.04e+03 6.31e-01 2.77e+01 19.183s
9000 +4.36845327e+04 +4.19595270e+04 1.73e+03 4.43e-01 2.02e+01 21.024s
10000 +4.36066182e+04 +4.19466670e+04 1.66e+03 3.40e-01 1.34e+01 22.862s
11000 +4.34340425e+04 +4.19473069e+04 1.49e+03 2.98e-01 1.10e+01 24.686s
12000 +4.33650676e+04 +4.19487325e+04 1.42e+03 2.04e-01 1.08e+01 26.510s
13000 +4.32280007e+04 +4.19498534e+04 1.28e+03 2.09e-01 1.01e+01 28.336s
14000 +4.31635430e+04 +4.19502678e+04 1.21e+03 1.57e-01 9.38e+00 30.160s
15000 +4.29279300e+04 +4.19528406e+04 9.75e+02 1.49e-01 1.43e+01 31.988s
16000 +4.26113016e+04 +4.19548002e+04 6.57e+02 1.44e-01 2.02e+01 33.815s
17000 +4.23855126e+04 +4.19542966e+04 4.31e+02 1.58e-01 2.21e+01 35.639s
18000 +4.22919321e+04 +4.19555036e+04 3.36e+02 1.36e-01 2.10e+01 37.467s
19000 +4.22261674e+04 +4.19541632e+04 2.72e+02 1.21e-01 1.87e+01 39.296s
20000 +4.21221562e+04 +4.19535454e+04 1.69e+02 1.07e-01 1.61e+01 41.125s
21000 +4.21004838e+04 +4.19532853e+04 1.47e+02 8.99e-02 1.41e+01 42.954s
22000 +4.20546042e+04 +4.19533260e+04 1.01e+02 6.65e-02 1.20e+01 44.781s
23000 +4.19625290e+04 +4.19515572e+04 1.10e+01 6.75e-02 9.74e+00 46.613s
24000 +4.19716938e+04 +4.19517660e+04 1.99e+01 5.25e-02 9.30e+00 48.442s
25000 +4.19650576e+04 +4.19516001e+04 1.35e+01 4.44e-02 8.43e+00 50.269s
26000 +4.19744741e+04 +4.19512414e+04 2.32e+01 3.01e-02 7.38e+00 52.100s
27000 +4.19498816e+04 +4.19510921e+04 1.21e+00 2.62e-02 6.18e+00 53.928s
28000 +4.19202749e+04 +4.19510622e+04 3.08e+01 2.82e-02 5.27e+00 55.756s
29000 +4.19200158e+04 +4.19510685e+04 3.11e+01 2.35e-02 4.64e+00 57.587s
30000 +4.19339749e+04 +4.19510884e+04 1.71e+01 2.00e-02 4.13e+00 59.415s
31000 +4.19372488e+04 +4.19510732e+04 1.38e+01 2.05e-02 3.65e+00 61.245s
32000 +4.19450298e+04 +4.19509837e+04 5.95e+00 1.86e-02 3.32e+00 63.073s
33000 +4.19377997e+04 +4.19509953e+04 1.32e+01 1.68e-02 3.08e+00 64.905s
34000 +4.19116770e+04 +4.19509917e+04 3.93e+01 2.92e-02 2.66e+00 66.736s
35000 +4.19171306e+04 +4.19510260e+04 3.39e+01 3.93e-02 2.08e+00 68.563s
36000 +4.19018061e+04 +4.19509506e+04 4.91e+01 4.33e-02 1.68e+00 70.392s
37000 +4.19288702e+04 +4.19509034e+04 2.20e+01 4.23e-02 1.34e+00 72.220s
38000 +4.19244557e+04 +4.19508715e+04 2.64e+01 4.03e-02 1.10e+00 74.051s
39000 +4.19356704e+04 +4.19508763e+04 1.52e+01 3.77e-02 9.55e-01 75.887s
40000 +4.19165846e+04 +4.19508814e+04 3.43e+01 3.66e-02 8.39e-01 77.722s
41000 +4.19203713e+04 +4.19508940e+04 3.05e+01 3.27e-02 7.23e-01 79.555s
42000 +4.19118138e+04 +4.19508570e+04 3.90e+01 2.82e-02 6.40e-01 81.390s
43000 +4.19373738e+04 +4.19508528e+04 1.35e+01 2.25e-02 5.75e-01 83.226s
44000 +4.19374643e+04 +4.19508963e+04 1.34e+01 2.25e-02 5.16e-01 85.059s
45000 +4.19347222e+04 +4.19509136e+04 1.62e+01 1.94e-02 4.71e-01 86.897s
46000 +4.19361199e+04 +4.19508517e+04 1.47e+01 1.72e-02 4.46e-01 88.731s
47000 +4.19325144e+04 +4.19508694e+04 1.84e+01 1.76e-02 4.14e-01 90.565s
48000 +4.19313102e+04 +4.19508622e+04 1.96e+01 1.68e-02 3.63e-01 92.401s
49000 +4.19345851e+04 +4.19508529e+04 1.63e+01 1.51e-02 3.24e-01 94.236s
50000 +4.19391543e+04 +4.19508554e+04 1.17e+01 1.36e-02 3.02e-01 96.069s
51000 +4.19414688e+04 +4.19508667e+04 9.40e+00 1.21e-02 2.89e-01 97.903s
52000 +4.19430661e+04 +4.19508659e+04 7.80e+00 1.12e-02 2.79e-01 99.736s
53000 +4.19416350e+04 +4.19508654e+04 9.23e+00 1.05e-02 2.68e-01 101.570s
53800 +4.19428379e+04 +4.19508666e+04 8.03e+00 9.98e-03 2.58e-01 103.037s
LP Solver status: Optimal
Primal objective: +4.19428379e+04
Dual objective: +4.19508666e+04
Duality gap (abs/rel): +8.03e+00 / +9.57e-05
Primal infeasibility (abs/rel): +9.98e-03 / +9.02e-07
Dual infeasibility (abs/rel): +2.58e-01 / +3.51e-09
PDLP finished
Status: Optimal Objective: 4.19428379e+04 Iterations: 53800 Time: 98.968s, Total time 103.042s
Post-solve status: Post solved solution violates constraints. This is most likely due to different tolerances.
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