Sample log file from the augmented system solver
Shows a typical log file from the augmented system solver.
Consider this model of a nonconvex quadratic program (QP) in LP file format.
Minimize
OBJ.FUNC: [ 2 x * y ] / 2
Subject To
R1: x - y < = 1
R2: x - y > = -1
R3: x + y < = 1
R4: x + y > = -1
Bounds
x free
y free
End
The objective function of that model includes a quadratic term that is not positive semi-definite. In such a case, CPLEX can apply an augmented system solver in the barrier optimizer.
In particular, if you apply the optimality target parameter with a value of 2, then CPLEX searches for a solution that satisfies first-order optimality conditions, but is not necessarily globally optimal.
Here is an example of a log file from the augmented system solver on that model:
Number of nonzeros in lower triangle of Q = 1
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.02 sec. (0.00 ticks)
Summary statistics for factor of Q:
Rows in Factor = 2
Integer space required = 2
Total nonzeros in factor = 3
Total FP ops to factor = 5
Note: Q in objective is not positive semi-definite.
Tried aggregator 1 time.
No QP presolve or aggregator reductions.
Presolve time = 0.02 sec. (0.00 ticks)
Summary statistics for factor of Augmented system:
Rows in Factor = 6
Integer space required = 0
Total nonzeros in factor = 21
Total FP ops to factor = 91
Itn Primal Obj Dual Obj Prim Inf Dual Inf Comple
0 1.2325952e-032 -1.2325952e-032 3.33e-016 4.00e+000 1.00e+000
1 -1.3681779e-033 -3.9837078e-014 2.22e-016 2.00e-003 5.00e-004
2 -8.6025148e-023 -4.0000199e-014 4.44e-016 1.00e-006 2.50e-007
3 -5.6343179e-022 -3.9999999e-014 1.11e-016 5.47e-010 1.25e-010
Barrier time = 0.03 sec. (0.03 ticks)
Total time on 8 threads = 0.03 sec. (0.03 ticks)
Barrier - Satisfies first-order optimality conditions: Objective = -5.634317873
4e-022
Solution time = 0.03 sec. Iterations = 3
Deterministic time = 0.03 ticks (0.93 ticks/sec)