Log interpretation¶

All interfaces use the same solver log. Logging is controlled by OutputFlag in Python, verbose in Julia and C, and --verbose or --quiet on the command line.

The example uses CUDA with feasibility polishing disabled. Timings depend on the problem, GPU, and system configuration.

Complete solver log

---------------------------------------------------------------------------------------
                                    cuPDLPx v0.3.0
                        A GPU-Accelerated First-Order LP Solver
               (c) Haihao Lu, Massachusetts Institute of Technology, 2025
---------------------------------------------------------------------------------------
Problem: 17013 rows, 200 columns, 104811 nonzeros
Settings:
  iter_limit         : 2147483647
  time_limit         : 3600.00 sec
  eps_opt            : 1.0e-04
  eps_feas           : 1.0e-04
  spmv_backend       : cusparseSpMVOp (auto)

Running presolver (PSLP v0.0.8)...
  status          : REDUCED
  presolve time   : 0.00853 sec
  reduced problem : 16997 rows, 200 columns, 104747 nonzeros

Preconditioning
  Ruiz scaling (10 iterations)
  Pock-Chambolle scaling (alpha=1.0000)
  Bound-objective scaling

---------------------------------------------------------------------------------------
   runtime     |     objective      |   absolute residuals    |   relative residuals
  iter   time  |  pr obj    du obj  |  pr res  du res   gap   |  pr res  du res   gap
---------------------------------------------------------------------------------------
     0 0.0e+00 |  0.0e+00   0.0e+00 | 0.0e+00 0.0e+00 0.0e+00 | 0.0e+00 0.0e+00 0.0e+00
   200 0.0e+00 | -1.3e+02  -1.2e+02 | 1.1e+00 2.5e-01 9.7e+00 | 8.5e-03 1.7e-02 3.9e-02
   400 8.7e-03 | -1.2e+02  -1.2e+02 | 2.3e-01 7.6e-02 9.2e-01 | 1.7e-03 5.0e-03 3.8e-03
   600 1.2e-02 | -1.2e+02  -1.2e+02 | 4.6e-02 8.5e-02 5.2e-03 | 3.5e-04 5.6e-03 2.1e-05
   800 1.5e-02 | -1.2e+02  -1.2e+02 | 2.5e-02 4.7e-02 3.3e-02 | 1.9e-04 3.1e-03 1.4e-04
  1000 1.8e-02 | -1.2e+02  -1.2e+02 | 1.2e-02 3.4e-02 7.3e-03 | 8.8e-05 2.2e-03 3.0e-05
  1200 2.1e-02 | -1.2e+02  -1.2e+02 | 4.3e-03 2.5e-02 7.6e-04 | 3.2e-05 1.6e-03 3.1e-06
  1400 2.4e-02 | -1.2e+02  -1.2e+02 | 3.1e-03 1.9e-02 1.4e-03 | 2.4e-05 1.3e-03 5.9e-06
  1600 2.7e-02 | -1.2e+02  -1.2e+02 | 3.2e-04 1.8e-02 2.6e-03 | 2.4e-06 1.2e-03 1.1e-05
  1800 3.0e-02 | -1.2e+02  -1.2e+02 | 2.8e-04 1.2e-02 6.5e-03 | 2.1e-06 8.0e-04 2.7e-05
  2000 3.3e-02 | -1.2e+02  -1.2e+02 | 2.1e-04 1.3e-02 3.5e-03 | 1.6e-06 8.3e-04 1.4e-05
  2200 3.6e-02 | -1.2e+02  -1.2e+02 | 3.0e-03 1.1e-02 5.8e-03 | 2.3e-05 7.2e-04 2.4e-05
  2400 4.0e-02 | -1.2e+02  -1.2e+02 | 3.1e-03 5.9e-03 1.9e-03 | 2.4e-05 3.9e-04 7.8e-06
  2600 4.3e-02 | -1.2e+02  -1.2e+02 | 2.2e-03 3.1e-03 1.4e-03 | 1.7e-05 2.1e-04 5.7e-06
  2800 4.6e-02 | -1.2e+02  -1.2e+02 | 1.0e-03 2.1e-03 1.7e-03 | 7.6e-06 1.4e-04 6.8e-06
  3000 4.8e-02 | -1.2e+02  -1.2e+02 | 6.4e-04 3.6e-04 4.6e-04 | 4.9e-06 2.4e-05 1.9e-06
---------------------------------------------------------------------------------------
Solution Summary
  Status                 : OPTIMAL
  Presolve time          : 0.00853 sec
  Precondition time      : 0.003735 sec
  Solve time             : 0.0517 sec
  Iterations             : 3000
  Primal objective       : -121.2216698
  Dual objective         : -121.2221271
  Objective gap          : 1.879e-06
  Primal infeas          : 4.889e-06
  Dual infeas            : 2.399e-05

Problem and settings¶

---------------------------------------------------------------------------------------
                                    cuPDLPx v0.3.0
                        A GPU-Accelerated First-Order LP Solver
               (c) Haihao Lu, Massachusetts Institute of Technology, 2025
---------------------------------------------------------------------------------------
Problem: 17013 rows, 200 columns, 104811 nonzeros
Settings:
  iter_limit         : 2147483647
  time_limit         : 3600.00 sec
  eps_opt            : 1.0e-04
  eps_feas           : 1.0e-04
  spmv_backend       : cusparseSpMVOp (auto)

The problem dimensions, four core settings, and selected sparse matrix–vector backend are always shown. Additional settings appear when they differ from their defaults. See Parameters for the corresponding interface names.

Presolve and preconditioning¶

Running presolver (PSLP v0.0.8)...
  status          : REDUCED
  presolve time   : 0.00853 sec
  reduced problem : 16997 rows, 200 columns, 104747 nonzeros

Preconditioning
  Ruiz scaling (10 iterations)
  Pock-Chambolle scaling (alpha=1.0000)
  Bound-objective scaling

REDUCED means that presolve produced an equivalent smaller LP. Postsolve recovers the solution vectors for the original LP. The reported residuals and gap are computed on the presolved LP.

Preconditioning rescales the LP before the main iteration. Its work is not included in the PDHG iteration count.

Progress table¶

For this example, the iteration log is:

---------------------------------------------------------------------------------------
   runtime     |     objective      |   absolute residuals    |   relative residuals
  iter   time  |  pr obj    du obj  |  pr res  du res   gap   |  pr res  du res   gap
---------------------------------------------------------------------------------------
     0 0.0e+00 |  0.0e+00   0.0e+00 | 0.0e+00 0.0e+00 0.0e+00 | 0.0e+00 0.0e+00 0.0e+00
   200 0.0e+00 | -1.3e+02  -1.2e+02 | 1.1e+00 2.5e-01 9.7e+00 | 8.5e-03 1.7e-02 3.9e-02
   400 8.7e-03 | -1.2e+02  -1.2e+02 | 2.3e-01 7.6e-02 9.2e-01 | 1.7e-03 5.0e-03 3.8e-03
   600 1.2e-02 | -1.2e+02  -1.2e+02 | 4.6e-02 8.5e-02 5.2e-03 | 3.5e-04 5.6e-03 2.1e-05
   800 1.5e-02 | -1.2e+02  -1.2e+02 | 2.5e-02 4.7e-02 3.3e-02 | 1.9e-04 3.1e-03 1.4e-04
  1000 1.8e-02 | -1.2e+02  -1.2e+02 | 1.2e-02 3.4e-02 7.3e-03 | 8.8e-05 2.2e-03 3.0e-05
  1200 2.1e-02 | -1.2e+02  -1.2e+02 | 4.3e-03 2.5e-02 7.6e-04 | 3.2e-05 1.6e-03 3.1e-06
  1400 2.4e-02 | -1.2e+02  -1.2e+02 | 3.1e-03 1.9e-02 1.4e-03 | 2.4e-05 1.3e-03 5.9e-06
  1600 2.7e-02 | -1.2e+02  -1.2e+02 | 3.2e-04 1.8e-02 2.6e-03 | 2.4e-06 1.2e-03 1.1e-05
  1800 3.0e-02 | -1.2e+02  -1.2e+02 | 2.8e-04 1.2e-02 6.5e-03 | 2.1e-06 8.0e-04 2.7e-05
  2000 3.3e-02 | -1.2e+02  -1.2e+02 | 2.1e-04 1.3e-02 3.5e-03 | 1.6e-06 8.3e-04 1.4e-05
  2200 3.6e-02 | -1.2e+02  -1.2e+02 | 3.0e-03 1.1e-02 5.8e-03 | 2.3e-05 7.2e-04 2.4e-05
  2400 4.0e-02 | -1.2e+02  -1.2e+02 | 3.1e-03 5.9e-03 1.9e-03 | 2.4e-05 3.9e-04 7.8e-06
  2600 4.3e-02 | -1.2e+02  -1.2e+02 | 2.2e-03 3.1e-03 1.4e-03 | 1.7e-05 2.1e-04 5.7e-06
  2800 4.6e-02 | -1.2e+02  -1.2e+02 | 1.0e-03 2.1e-03 1.7e-03 | 7.6e-06 1.4e-04 6.8e-06
  3000 4.8e-02 | -1.2e+02  -1.2e+02 | 6.4e-04 3.6e-04 4.6e-04 | 4.9e-06 2.4e-05 1.9e-06
---------------------------------------------------------------------------------------

Column	Meaning
`iter`	Total PDHG iterations completed.
`time`	Elapsed main-solve time in seconds.
`pr obj`	Primal objective value.
`du obj`	Dual objective value.
`pr res`	Primal feasibility residual.
`du res`	Dual feasibility residual.
`gap`	Primal–dual objective gap.

The log reports absolute and relative primal residuals, dual residuals, and gaps. The optimality test requires the relative residuals to be below FeasibilityTol and the relative gap to be below OptimalityTol. See Termination criteria for the formulas.

TermCheckFreq sets the termination-check interval, 200 in this example. Progress is logged at these checks, with fewer rows printed as the iteration count grows. Restarts are checked at the same interval and have no separate log marker. Residuals and objective values need not decrease monotonically.

Feasibility polishing¶

When feasibility polishing runs, the log shows separate primal and dual tables with objective values and absolute and relative residuals. The polishing summary reports each phase's status, iteration count, and time.

Polishing can reduce feasibility residuals while increasing the primal–dual gap. The main solve's termination status is unchanged. See Feasibility polishing.

Solution summary¶

Read the final summary in this order:

Status: check why the solver stopped. OPTIMAL means it reached the requested accuracy; a time or iteration limit does not establish that.
Primal and dual residuals: compare Primal infeas and Dual infeas with FeasibilityTol.
Objective gap: compare Objective gap with OptimalityTol.

For example:

Solution Summary
  Status                 : OPTIMAL
  Presolve time          : 0.00853 sec
  Precondition time      : 0.003735 sec
  Solve time             : 0.0517 sec
  Iterations             : 3000
  Primal objective       : -121.2216698
  Dual objective         : -121.2221271
  Objective gap          : 1.879e-06
  Primal infeas          : 4.889e-06
  Dual infeas            : 2.399e-05

Both residuals and the relative gap are below the requested 1e-4 tolerances.

The fields have the following meanings:

Field	Meaning
`Status`	Termination reason, such as `OPTIMAL`, `TIME_LIMIT`, or `ITERATION_LIMIT`.
`Presolve time`	Time spent in PSLP, shown when presolve is enabled.
`Precondition time`	Time spent scaling the LP and preparing the scaled problem.
`Solve time`	Time spent in the main iteration.
`Iterations`	Total main-solve iteration count.
`Primal objective`, `Dual objective`	Final objective values, including the objective constant and original objective sense.
`Objective gap`	Final relative primal–dual gap on the presolved LP when presolve is enabled.
`Primal infeas`, `Dual infeas`	Final relative residuals on the presolved LP when presolve is enabled.

Primal infeas and Dual infeas are residual magnitudes. Use Status to determine whether the solver detected infeasibility. See Results and status for termination reasons and result fields.