Optimal Interior-point solution but failed Basic solution

1

I’m solving a large LP problem (Calling Mosek unknown: 89524 variables, 3425 equality constraints) and there are several nearly zero elements in the matrix. I get the following report:

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -2.1236211578e+00 nrm: 2e+02 Viol. con: 2e-07 var: 0e+00
Dual. obj: -2.1236210010e+00 nrm: 4e+03 Viol. con: 0e+00 var: 8e-11

Basic solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 2e+02 var: 0e+00
Dual. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 3e+02
Optimizer summary
Optimizer - time: 49.05
Interior-point - iterations : 25 time: 48.95
Basis identification - time: 47.38
Primal - iterations : 579 time: 0.00
Dual - iterations : 322 time: 0.14
Clean primal - iterations : 52826 time: 47.17
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00

Status: Failed
Optimal value (cvx_optval): NaN

My question is that, it seems that the interior-point method solves the problem successfully, but why the final status is “Failed”? How should I handle this? Should I restrict to the interior-point method
by passing

cvx_solver_settings(‘MSK_IPAR_OPTIMIZER’, ‘MSK_OPTIMIZER_INTPNT’)

2

If the optimal basis is very ill conditioned then BI can fail for that reason. So most likely it is a numerical issue causing the failure. I cannot be more precise without being able to run the problem.

If you want to turn BI off, then use the parameter

https://docs.mosek.com/9.1/toolbox/parameters.html#mosek.iparam.intpnt_basis

3

Thanks so much, Erling! Very much appreciate it!