# Mosek solves a linear feasibility problem during presolve

#1

I am using MOSEK and CVX to fit a function to a given data, and in many cases MOSEK is able to solve linear feasibility problem during presolve. I was wondering if I could find a feasible solution without using MOSEK based on this knowledge. I am attaching the solver log below. Thanks.

## Calling Mosek 7.1.0.12: 20000 variables, 500 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 7.1.0.12 (Build date: 2014-12-12 11:23:25)
Platform: Windows/64-X86

Computer
Platform : Windows/64-X86
Cores : 2

Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 500
Cones : 0
Scalar variables : 20000
Matrix variables : 0
Integer variables : 0

Optimizer started.
Interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Eliminator - elim’s : 0
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Interior-point optimizer terminated. Time: 0.03.

Optimizer terminated. Time: 0.05

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 0.0000000000e+000 Viol. con: 0e+000 var: 0e+000
Dual. obj: 0.0000000000e+000 Viol. con: 0e+000 var: 3e-014

Basic solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 0.0000000000e+000 Viol. con: 0e+000 var: 0e+000
Dual. obj: 0.0000000000e+000 Viol. con: 0e+000 var: 3e-014
Optimizer summary
Optimizer - time: 0.05
Interior-point - iterations : 0 time: 0.03
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Clean primal-dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Primal-dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00

Status: Solved
Optimal value (cvx_optval): -0

(Erling D.Andersen) #2

Sure you can just implement a presolve like Mosek has.