Logging
Pre-Execution Logging
The solver logs all the parameter information before execution:
------------------------------------------------------------------------
DuaLip v1.0 2021
Dual Decomposition based Linear Program Solver
------------------------------------------------------------------------
Settings:
--driver.objectiveClass com.linkedin.dualip.problem.MooSolverDualObjectiveFunction
--driver.solverOutputPath /dualip/test
--driver.gamma 1E-6
--driver.outputFormat avro
--driver.projectionType simplex
--driver.verbosity 1
--input.ACblocksPath /unit-test/moo/60/data
--input.vectorBPath /unit-test/moo/60/constraint
--input.format avro
--optimizer.solverType LBFGSB
--optimizer.dualTolerance 1E-8
--optimizer.slackTolerance 5E-6
--optimizer.maxIter 100
In-Execution Logging
The solver prints the following information during execution. (Note: Which variables are reported depends on the solver.)
Variables |
Description |
|---|---|
|
The number of calls to compute the gradient in the solver. |
|
Iteration number. |
|
Dual objective value (including regularization term). |
|
Primal objective value without regularization term, i.e. \(c^\top x\). |
|
\(\max_j \{ (Ax-b)_j / (1 + |b_j|)\}\). |
\(\lambda(Ax-b)\) |
\(\lambda^\top (Ax - b)\). |
\(\frac{\gamma}{2}||x||^2\) |
Regularization term. |
|
\(\max_{j: \lambda_j \neq 0} | (Ax-b)_j | / (1 + |b_j|)\) (only over inequality constraints). |
|
\(\max_{j: \lambda_j = 0} \{ (Ax-b)_j, 0\} / (1 + |b_j|)\) (only over inequality constraints). |
|
Sum of constraint violations. |
|
Execution time of this iteration in seconds. |
|
Step size for the gradient optimizer. |
Termination Logging
The solver prints one of the four possible results at termination:
Status |
Description |
|---|---|
|
The algorithm has converged according to the convergence criteria. |
|
This happens when the dual objective has exceeded the primal upper bound. |
|
The solver has reached maximum number of iterations. Users can look at the log to determine if the results are good enough to be used. |
|
The solver failed during execution. Specific failure reason will be given in logs. |
We also show the number of iterations, the final primal and dual objective values and the number of active constraints.
Sample log
------------------------------------------------------------------------
DuaLip v1.0 2021
Dual Decomposition based Linear Program Solver
------------------------------------------------------------------------
Settings:
--driver.objectiveClass com.linkedin.dualip.problem.MooSolverDualObjectiveFunction
--driver.solverOutputPath /dualip/test
--driver.gamma 1E-6
--driver.outputFormat avro
--driver.projectionType simplex
--driver.verbosity 1
--input.ACblocksPath /unit-test/moo/60/data
--input.vectorBPath /unit-test/moo/60/constraint
--input.format avro
--optimizer.solverType LBFGSB
--optimizer.dualTolerance 1E-8
--optimizer.slackTolerance 5E-6
--optimizer.maxIter 100
Optimizer: LBFGSB solver
primalUpperBound: 2.50000000e-05, maxIter: 100, dualTolerance: 1.0E-8 slackTolerance: 5.0E-6
gradientCall: 0 iter: 0 dual_obj: -4.99999750e+01 cx: -5.00000000e+01 feasibility: 2.217486e+01 λ(Ax-b): 0.000000e+00 γ||x||/2: 2.500000e-05 max_pos_slack: -Infinity max_zero_slack: 2.217486e+01 abs_slack_sum: 3.146621e+01 time(sec): 5.135
gradientCall: 1 iter: 1 dual_obj: -4.99999750e+01 cx: -5.00000000e+01 feasibility: 2.217486e+01 λ(Ax-b): 0.000000e+00 γ||x||/2: 2.500000e-05 max_pos_slack: -Infinity max_zero_slack: 2.217486e+01 abs_slack_sum: 3.146621e+01 time(sec): 1.035
gradientCall: 2 iter: 1 dual_obj: -1.36522019e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.265221e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 2.079
gradientCall: 3 iter: 1 dual_obj: -1.36522019e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.265221e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.038
gradientCall: 4 iter: 2 dual_obj: -1.36522019e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.265221e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.552
gradientCall: 5 iter: 2 dual_obj: -1.34925665e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.249257e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.945
gradientCall: 6 iter: 2 dual_obj: -1.34127487e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.241275e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.392
gradientCall: 7 iter: 2 dual_obj: -1.32930221e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.229303e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.279
gradientCall: 8 iter: 2 dual_obj: -1.31134322e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.211344e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.580
gradientCall: 9 iter: 2 dual_obj: -1.28440474e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.184405e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.965
gradientCall: 10 iter: 2 dual_obj: -1.24399701e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.143998e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.690
gradientCall: 11 iter: 2 dual_obj: -1.18338541e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -1.083386e+01 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.832
gradientCall: 12 iter: 2 dual_obj: -1.09246802e+01 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -9.924686e+00 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.559
gradientCall: 13 iter: 2 dual_obj: -9.56091935e+00 cx: -1.00000000e+00 feasibility: -2.833599e-01 λ(Ax-b): -8.560925e+00 γ||x||/2: 5.400000e-06 max_pos_slack: 2.833599e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.265
gradientCall: 14 iter: 2 dual_obj: -7.68762043e+00 cx: -2.00000000e+00 feasibility: -2.473638e-01 λ(Ax-b): -5.687626e+00 γ||x||/2: 5.800000e-06 max_pos_slack: 2.473638e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.594
gradientCall: 15 iter: 2 dual_obj: -7.68762043e+00 cx: -2.00000000e+00 feasibility: -2.473638e-01 λ(Ax-b): -5.687626e+00 γ||x||/2: 5.800000e-06 max_pos_slack: 2.473638e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.231
gradientCall: 16 iter: 3 dual_obj: -7.68762043e+00 cx: -2.00000000e+00 feasibility: -2.473638e-01 λ(Ax-b): -5.687626e+00 γ||x||/2: 5.800000e-06 max_pos_slack: 2.473638e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.664
gradientCall: 17 iter: 3 dual_obj: -4.99999750e+01 cx: -5.00000000e+01 feasibility: 2.217486e+01 λ(Ax-b): 0.000000e+00 γ||x||/2: 2.500000e-05 max_pos_slack: -Infinity max_zero_slack: 2.217486e+01 abs_slack_sum: 3.146621e+01 time(sec): 0.859
gradientCall: 18 iter: 3 dual_obj: -5.59665447e+00 cx: -7.00000000e+00 feasibility: 1.518062e-01 λ(Ax-b): 1.403338e+00 γ||x||/2: 7.800000e-06 max_pos_slack: 1.518062e-01 max_zero_slack: -Infinity abs_slack_sum: 2.154136e-01 time(sec): 0.611
gradientCall: 19 iter: 3 dual_obj: -5.59665447e+00 cx: -7.00000000e+00 feasibility: 1.518062e-01 λ(Ax-b): 1.403338e+00 γ||x||/2: 7.800000e-06 max_pos_slack: 1.518062e-01 max_zero_slack: -Infinity abs_slack_sum: 2.154136e-01 time(sec): 0.385
gradientCall: 20 iter: 4 dual_obj: -5.59665447e+00 cx: -7.00000000e+00 feasibility: 1.518062e-01 λ(Ax-b): 1.403338e+00 γ||x||/2: 7.800000e-06 max_pos_slack: 1.518062e-01 max_zero_slack: -Infinity abs_slack_sum: 2.154136e-01 time(sec): 0.448
gradientCall: 21 iter: 4 dual_obj: -5.84994265e+00 cx: -4.00000000e+00 feasibility: -1.278211e-01 λ(Ax-b): -1.849949e+00 γ||x||/2: 6.600000e-06 max_pos_slack: 1.278211e-01 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.024
gradientCall: 22 iter: 4 dual_obj: -5.53061009e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.306171e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.842
gradientCall: 23 iter: 4 dual_obj: -5.53061009e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.306171e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.021
gradientCall: 24 iter: 5 dual_obj: -5.53061009e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.306171e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.855
gradientCall: 25 iter: 5 dual_obj: -5.51271230e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.127193e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.645
gradientCall: 26 iter: 5 dual_obj: -5.50376340e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.037704e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.730
gradientCall: 27 iter: 5 dual_obj: -5.50964555e+00 cx: -6.00000000e+00 feasibility: 4.952939e-02 λ(Ax-b): 4.903471e-01 γ||x||/2: 7.400000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 7.028239e-02 time(sec): 0.779
gradientCall: 28 iter: 5 dual_obj: -5.50037908e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.003861e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.915
gradientCall: 29 iter: 5 dual_obj: -5.50110192e+00 cx: -6.00000000e+00 feasibility: 4.952939e-02 λ(Ax-b): 4.988907e-01 γ||x||/2: 7.400000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 7.028239e-02 time(sec): 2.274
gradientCall: 30 iter: 5 dual_obj: -5.50002401e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.000310e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.460
gradientCall: 31 iter: 5 dual_obj: -5.50012824e+00 cx: -6.00000000e+00 feasibility: 4.952939e-02 λ(Ax-b): 4.998644e-01 γ||x||/2: 7.400000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 7.028239e-02 time(sec): 1.187
gradientCall: 32 iter: 5 dual_obj: -5.49999490e+00 cx: -6.00000000e+00 feasibility: 4.952939e-02 λ(Ax-b): 4.999977e-01 γ||x||/2: 7.400000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 7.028239e-02 time(sec): 0.341
gradientCall: 33 iter: 5 dual_obj: -5.49999588e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.000029e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.770
gradientCall: 34 iter: 5 dual_obj: -5.49999301e+00 cx: -5.82333310e+00 feasibility: 3.202898e-02 λ(Ax-b): 3.233328e-01 γ||x||/2: 7.242060e-06 max_pos_slack: 3.202898e-02 max_zero_slack: -Infinity abs_slack_sum: 4.544925e-02 time(sec): 0.691
gradientCall: 35 iter: 5 dual_obj: -5.49999301e+00 cx: -5.82333310e+00 feasibility: 3.202898e-02 λ(Ax-b): 3.233328e-01 γ||x||/2: 7.242060e-06 max_pos_slack: 3.202898e-02 max_zero_slack: -Infinity abs_slack_sum: 4.544925e-02 time(sec): 0.758
gradientCall: 36 iter: 6 dual_obj: -5.49999301e+00 cx: -5.82333310e+00 feasibility: 3.202898e-02 λ(Ax-b): 3.233328e-01 γ||x||/2: 7.242060e-06 max_pos_slack: 3.202898e-02 max_zero_slack: -Infinity abs_slack_sum: 4.544925e-02 time(sec): 0.713
gradientCall: 37 iter: 6 dual_obj: -5.51201647e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.120235e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.748
gradientCall: 38 iter: 6 dual_obj: -5.50127583e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.012828e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 1.102
gradientCall: 39 iter: 6 dual_obj: -5.50012959e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.001366e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.500
gradientCall: 40 iter: 6 dual_obj: -5.50000727e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.000143e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.686
gradientCall: 41 iter: 6 dual_obj: -5.49999421e+00 cx: -5.00000000e+00 feasibility: -4.952939e-02 λ(Ax-b): -5.000012e-01 γ||x||/2: 7.000000e-06 max_pos_slack: 4.952939e-02 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.484
gradientCall: 42 iter: 6 dual_obj: -5.49999295e+00 cx: -5.44549277e+00 feasibility: -5.399420e-03 λ(Ax-b): -5.450721e-02 γ||x||/2: 7.029980e-06 max_pos_slack: 5.399420e-03 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.777
gradientCall: 43 iter: 6 dual_obj: -5.49999295e+00 cx: -5.44549277e+00 feasibility: -5.399420e-03 λ(Ax-b): -5.450721e-02 γ||x||/2: 7.029980e-06 max_pos_slack: 5.399420e-03 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.735
gradientCall: 44 iter: 7 dual_obj: -5.49999295e+00 cx: -5.44549277e+00 feasibility: -5.399420e-03 λ(Ax-b): -5.450721e-02 γ||x||/2: 7.029980e-06 max_pos_slack: 5.399420e-03 max_zero_slack: -Infinity abs_slack_sum: 0.000000e+00 time(sec): 0.925
gradientCall: 45 iter: 7 dual_obj: -5.49999295e+00 cx: -5.50000000e+00 feasibility: 9.492812e-13 λ(Ax-b): 9.583005e-12 γ||x||/2: 7.050000e-06 max_pos_slack: 9.492812e-13 max_zero_slack: -Infinity abs_slack_sum: 1.347034e-12 time(sec): 0.934
gradientCall: 46 iter: 7 dual_obj: -5.49999295e+00 cx: -5.50000000e+00 feasibility: 9.492812e-13 λ(Ax-b): 9.583005e-12 γ||x||/2: 7.050000e-06 max_pos_slack: 9.492812e-13 max_zero_slack: -Infinity abs_slack_sum: 1.347034e-12 time(sec): 1.155
Total LBFGS iterations: 7
Status:Converged
Total number of iterations: 47
Primal: -5.44548574018906
Dual: -5.499992951782625
Number of Active Constraints: 1