Integrate PSLP Presolver by ZedongPeng · Pull Request #41 · MIT-Lu-Lab/cuPDLPx

ZedongPeng · 2025-11-24T22:00:14Z

Description

This PR adds optional support for the PSLP presolver in cuPDLPx. When enabled (by default), the problem is presolved with PSLP before being sent to the GPU.

Summary

The integration works correctly, and PSLP significantly reduces the problem size (rows/cols/nnz). However, the presolved problem currently takes more PDHG iterations to converge.

Any feedback on whether this behavior is expected with PSLP would be appreciated. @dance858

Output

Without PSLP presolve.

$ ./build/cupdlpx L1_sixm250obs.mps.gz test/ -v
---------------------------------------------------------------------------------------
                                    cuPDLPx v0.1.3                                    
                        A GPU-Accelerated First-Order LP Solver                        
               (c) Haihao Lu, Massachusetts Institute of Technology, 2025              
---------------------------------------------------------------------------------------
problem:
  variables     : 428032
  constraints   : 986069
  nnz(A)        : 4280320
settings:
  iter_limit         : 2147483647
  time_limit         : 3600.00 sec
  eps_opt            : 1.0e-04
  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 4.2e-04 |  0.0e+00   0.0e+00 | 0.0e+00 4.1e+00 0.0e+00 | 0.0e+00 8.1e-01 0.0e+00 
    10 2.9e-03 |  5.3e+03   6.6e+08 | 4.7e+03 4.0e+04 6.6e+08 | 4.7e+03 7.7e+03 1.0e+00 
    20 5.3e-03 |  6.8e+03   3.3e+08 | 1.9e+03 1.9e+04 3.3e+08 | 1.9e+03 3.7e+03 1.0e+00 
    30 7.8e-03 |  8.2e+03   2.3e+08 | 9.6e+02 1.3e+04 2.3e+08 | 9.6e+02 2.6e+03 1.0e+00 
    40 1.0e-02 |  8.4e+03   1.5e+08 | 1.2e+03 9.0e+03 1.5e+08 | 1.2e+03 1.7e+03 1.0e+00 
    50 1.3e-02 |  8.0e+03   1.0e+08 | 4.6e+02 6.8e+03 1.0e+08 | 4.6e+02 1.3e+03 1.0e+00 
    60 1.5e-02 |  7.5e+03   9.5e+07 | 6.2e+02 5.8e+03 9.5e+07 | 6.2e+02 1.1e+03 1.0e+00 
    70 1.8e-02 |  7.5e+03   9.0e+07 | 4.7e+02 5.2e+03 9.0e+07 | 4.7e+02 1.0e+03 1.0e+00 
    80 2.0e-02 |  7.9e+03   8.4e+07 | 2.2e+02 4.8e+03 8.4e+07 | 2.2e+02 9.3e+02 1.0e+00 
    90 2.3e-02 |  8.1e+03   6.7e+07 | 4.4e+02 3.9e+03 6.7e+07 | 4.4e+02 7.6e+02 1.0e+00 
   100 2.5e-02 |  7.9e+03   5.3e+07 | 2.1e+02 3.4e+03 5.3e+07 | 2.1e+02 6.5e+02 1.0e+00 
...
 10000 2.2e+00 |  4.6e+03   4.6e+03 | 8.4e-03 3.0e-06 2.3e-01 | 8.4e-03 5.8e-07 2.5e-05 
 11000 2.4e+00 |  4.6e+03   4.6e+03 | 9.1e-03 2.7e-08 6.2e-04 | 9.1e-03 5.3e-09 6.7e-08 
 12000 2.6e+00 |  4.6e+03   4.6e+03 | 1.5e-04 1.1e-09 1.2e-04 | 1.5e-04 2.2e-10 1.3e-08 
---------------------------------------------------------------------------------------
Solution Summary
  Status        : OPTIMAL
  Iterations    : 12200
  Solve time    : 2.63 sec
  Primal obj    : 4629.462791
  Dual obj      : 4629.462716
  Primal infeas : 5.625e-05
  Dual infeas   : 1.478e-10

With PSLP presolve

$ ./build/cupdlpx /L1_sixm250obs.mps.gz test/ -v -p
---------------------------------------------------------------------------------------
                                    cuPDLPx v0.1.3                                    
                        A GPU-Accelerated First-Order LP Solver                        
               (c) Haihao Lu, Massachusetts Institute of Technology, 2025              
---------------------------------------------------------------------------------------
problem:
  variables     : 428032
  constraints   : 986069
  nnz(A)        : 4280320
settings:
  iter_limit         : 2147483647
  time_limit         : 3600.00 sec
  eps_opt            : 1.0e-04
  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   
---------------------------------------------------------------------------------------
Running Presolve...

               PSLP v0.0.1 - LP presolver 
        (c) Daniel Cederberg, Stanford University, 2025
Original problem:  986069 rows, 428032 columns, 4280320 nnz
Presolved problem: 721572 rows, 310389 columns, 3151786 nnz
Presolver init & run time : 0.151 seconds, 1.047 
Presolve finished. Reduced rows: 721572, cols: 310389
     0 4.1e-04 |  0.0e+00   0.0e+00 | 0.0e+00 6.9e+01 0.0e+00 | 0.0e+00 9.9e-01 0.0e+00 
    10 2.4e-03 |  5.4e+03   3.3e+08 | 4.5e+03 1.2e+05 3.3e+08 | 4.5e+03 1.8e+03 1.0e+00 
    20 4.3e-03 |  6.9e+03   2.0e+08 | 1.6e+03 5.7e+04 2.0e+08 | 1.6e+03 8.2e+02 1.0e+00 
    30 6.3e-03 |  8.3e+03   1.5e+08 | 9.2e+02 4.5e+04 1.5e+08 | 9.2e+02 6.5e+02 1.0e+00 
    40 8.3e-03 |  8.4e+03   7.5e+07 | 1.1e+03 3.3e+04 7.5e+07 | 1.1e+03 4.8e+02 1.0e+00 
    50 1.0e-02 |  7.9e+03   3.7e+07 | 3.5e+02 2.3e+04 3.7e+07 | 3.5e+02 3.4e+02 1.0e+00 
    60 1.2e-02 |  7.5e+03   4.7e+07 | 6.4e+02 1.8e+04 4.7e+07 | 6.4e+02 2.6e+02 1.0e+00 
    70 1.4e-02 |  7.6e+03   5.7e+07 | 3.6e+02 1.6e+04 5.7e+07 | 3.6e+02 2.3e+02 1.0e+00 
    80 1.6e-02 |  8.0e+03   5.1e+07 | 2.9e+02 1.6e+04 5.1e+07 | 2.9e+02 2.3e+02 1.0e+00 
    90 1.8e-02 |  8.0e+03   3.1e+07 | 3.9e+02 1.5e+04 3.1e+07 | 3.9e+02 2.1e+02 1.0e+00 
   100 2.0e-02 |  7.8e+03   2.1e+07 | 1.2e+02 1.2e+04 2.1e+07 | 1.2e+02 1.7e+02 1.0e+00 
...
 10000 1.7e+00 |  4.6e+03   4.6e+03 | 9.4e-01 8.7e-05 7.2e+00 | 9.4e-01 1.3e-06 7.8e-04 
 11000 1.9e+00 |  4.6e+03   4.6e+03 | 6.8e-01 3.4e-05 2.8e+00 | 6.8e-01 4.9e-07 3.0e-04 
 12000 2.1e+00 |  4.6e+03   4.6e+03 | 2.3e+00 3.6e-06 2.1e-02 | 2.3e+00 5.2e-08 2.2e-06 
 13000 2.2e+00 |  4.6e+03   4.6e+03 | 1.2e-01 7.4e-07 4.2e-02 | 1.2e-01 1.1e-08 4.5e-06 
 14000 2.4e+00 |  4.6e+03   4.6e+03 | 3.0e-03 4.6e-08 3.3e-03 | 3.0e-03 6.6e-10 3.5e-07 
 15000 2.6e+00 |  4.6e+03   4.6e+03 | 2.1e-04 1.0e-09 2.5e-05 | 2.1e-04 1.5e-11 2.7e-09 
---------------------------------------------------------------------------------------
Solution Summary
  Status        : OPTIMAL
  Iterations    : 15200
  Solve time    : 2.6 sec
  Primal obj    : 4629.462796
  Dual obj      : 4629.462801
  Primal infeas : 1.166e-05
  Dual infeas   : 6.269e-12
Postsolve time: 0.0149 seconds

Related PSLP issue:

TODO

Enable presolve by default.
Update readme.

src/presolve.c

dance858 · 2025-11-25T01:28:42Z

I think this looks correct, with one small exception (see my comment above).

At the moment, I don’t have a clear hypothesis about whether the presolved problem should require fewer or more iterations. Whenever you have the opportunity to run the benchmarks, it would be very interesting to hear your insights on the following:

Does the presolved problem require more iterations on the majority of instances?
Is there a noticeable difference depending on whether cuPDLPx is run at high vs. low accuracy?
It may be worth setting settings->relax_bounds = false to see whether keeping the bounds affects the iteration count. When this option is set to false, redundant bounds remain in the problem. (They are redundant in the sense that if the other primal constraints are satisfied, the bounds will be as well.) But who knows, perhaps cuPDLPx benefits from having these redundant bounds present during the projection step?

src/presolve.c

dance858 · 2025-11-25T02:06:34Z

I thought of something else. When PSLP fixes variables, it updates an offset in the objective. The offset is stored in presolver->prob->obj->offset. I think it makes sense to include this offset when evaluating the termination criteria inside cuPDLPx for the reduced problem.

ZedongPeng · 2025-11-25T06:29:37Z

I thought of something else. When PSLP fixes variables, it updates an offset in the objective. The offset is stored in presolver->prob->obj->offset. I think it makes sense to include this offset when evaluating the termination criteria inside cuPDLPx for the reduced problem.

@dance858 It might be better to add the definition of offset directly in the reduced problem. The Objective struct is defined in Problem.h, which I regard as an internal struct:
https://github.com/dance858/PSLP/blob/259ca2e1e1097c4acb36788d374e938bc00aafca/include/core/Problem.h#L31-L35

dance858 · 2025-11-25T13:19:46Z

Good point and I totally agree. I'm pushing up the fix now. The offset is stored in PresolvedProblem->obj_offset.

src/presolve.c

ZedongPeng · 2025-11-26T02:30:20Z

Hi @dance858 . I have updated the reduced cost computation in postsolve. Could you take a look and let me know if it looks correct?

… memory

add PSLP presolver

846822f

ZedongPeng requested a review from jinwen-yang November 24, 2025 22:15

dance858 reviewed Nov 25, 2025

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dance858 reviewed Nov 25, 2025

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ZedongPeng added 2 commits November 25, 2025 17:52

fix: correct the reduced cost in PSLP postsolve

ca4fda5

add presolve stats

81e40bb

ZedongPeng commented Nov 26, 2025

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src/presolve.c Outdated Show resolved Hide resolved

ZedongPeng added 9 commits November 26, 2025 01:18

test PSLP relax_bounds false

6ee68cf

remove PSLP_INF

4abff54

add presolve_setup_time and presolve_time record, improve reduce prob…

49a6e8f

… memory

set relax_bounds to True (default)

8673627

fix Segmentation fault when presolve detected infeasible

c8ba05d

refactor: PSLP presolve

7c58682

add verbose check for log

f68eef8

set use_presolve to true by default

3466c47

Merge branch 'main' into pslp-new

d52dccd

ZedongPeng changed the title ~~[WIP] Integrate PSLP Presolver~~ Integrate PSLP Presolver Dec 16, 2025

ZedongPeng added 6 commits December 16, 2025 12:27

rename use_presolve to presolve

7298fa6

refactor: add presolve in python interface

bc0cbdd

docs: add presolve in readme

9ca8061

feat: release v0.2.0

9b6d90a

fix: off-by-one iteration error and ensure consistent final metrics

97ad216

Merge branch 'main' into pslp-new

4ab953c

jinwen-yang approved these changes Dec 20, 2025

View reviewed changes

ZedongPeng merged commit b524c2a into MIT-Lu-Lab:main Dec 20, 2025

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Integrate PSLP Presolver#41

Integrate PSLP Presolver#41
ZedongPeng merged 18 commits intoMIT-Lu-Lab:mainfrom
ZedongPeng:pslp-new

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Description

Summary

Output

Related PSLP issue:

TODO

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