nagcpp::opt::handle_solve_lp_ipm Example
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E04MT, Interior point method for LP problems
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Begin of Options
Print File = 6 * d
Print Level = 2 * d
Print Options = Yes * d
Print Solution = All * U
Monitoring File = -1 * d
Monitoring Level = 4 * d
Lpipm Monitor Frequency = 1 * U
Infinite Bound Size = 1.00000E+20 * d
Task = Minimize * d
Stats Time = No * d
Lp Presolve = Yes * d
Lpipm Algorithm = Primal-dual * d
Lpipm Centrality Correctors = -6 * U
Lpipm Iteration Limit = 100 * d
Lpipm Max Iterative Refinement= 5 * d
Lpipm Scaling = Arithmetic * d
Lpipm Stop Tolerance = 1.00000E-10 * U
Lpipm Stop Tolerance 2 = 2.67452E-10 * d
Lpipm System Formulation = Auto * d
End of Options
Original Problem Statistics
Number of variables 7
Number of constraints 7
Free variables 0
Number of nonzeros 41
Presolved Problem Statistics
Number of variables 13
Number of constraints 7
Free variables 0
Number of nonzeros 47
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it| pobj | dobj | optim | feas | compl | mu | mcc | I
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0 -7.86591E-02 1.71637E-02 1.27E+00 1.06E+00 8.89E-02 1.5E-01
1 5.74135E-03 -2.24369E-02 6.11E-16 1.75E-01 2.25E-02 2.8E-02 0
2 1.96803E-02 1.37067E-02 5.06E-16 2.28E-02 2.91E-03 3.4E-03 0
3 2.15232E-02 1.96162E-02 7.71E-16 9.24E-03 1.44E-03 1.7E-03 0
4 2.30321E-02 2.28676E-02 1.15E-15 2.21E-03 2.97E-04 3.4E-04 0
5 2.35658E-02 2.35803E-02 8.61E-16 1.02E-04 8.41E-06 9.6E-06 0
6 2.35965E-02 2.35965E-02 4.99E-16 7.02E-08 6.35E-09 7.2E-09 0
Iteration 7
monit() reports good approximate solution (tol = 1.2e-08):
7 2.35965E-02 2.35965E-02 6.95E-16 3.52E-11 3.18E-12 3.6E-12 0
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Status: converged, an optimal solution found
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Final primal objective value 2.359648E-02
Final dual objective value 2.359648E-02
Absolute primal infeasibility 2.144028E-15
Relative primal infeasibility 6.945506E-16
Absolute dual infeasibility 5.084352E-11
Relative dual infeasibility 3.518607E-11
Absolute complementarity gap 2.685778E-11
Relative complementarity gap 3.175366E-12
Iterations 7
Primal variables:
idx Lower bound Value Upper bound
1 -1.00000E-02 -1.00000E-02 1.00000E-02
2 -1.00000E-01 -1.00000E-01 1.50000E-01
3 -1.00000E-02 3.00000E-02 3.00000E-02
4 -4.00000E-02 2.00000E-02 2.00000E-02
5 -1.00000E-01 -6.74853E-02 5.00000E-02
6 -1.00000E-02 -2.28013E-03 inf
7 -1.00000E-02 -2.34528E-04 inf
Box bounds dual variables:
idx Lower bound Value Upper bound Value
1 -1.00000E-02 3.30098E-01 1.00000E-02 0.00000E+00
2 -1.00000E-01 1.43844E-02 1.50000E-01 0.00000E+00
3 -1.00000E-02 0.00000E+00 3.00000E-02 9.09967E-02
4 -4.00000E-02 0.00000E+00 2.00000E-02 7.66124E-02
5 -1.00000E-01 3.51391E-11 5.00000E-02 0.00000E+00
6 -1.00000E-02 3.42902E-11 inf 0.00000E+00
7 -1.00000E-02 8.61040E-12 inf 0.00000E+00
Constraints dual variables:
idx Lower bound Value Upper bound Value
1 -1.30000E-01 0.00000E+00 -1.30000E-01 1.43111E+00
2 -inf 0.00000E+00 -4.90000E-03 4.00339E-10
3 -inf 0.00000E+00 -6.40000E-03 1.54305E-08
4 -inf 0.00000E+00 -3.70000E-03 3.80136E-10
5 -inf 0.00000E+00 -1.20000E-03 4.72629E-11
6 -9.92000E-02 1.50098E+00 inf 0.00000E+00
7 -3.00000E-03 1.51661E+00 2.00000E-03 0.00000E+00