echo on
n = 10;
A = randn(2*n,n);
b = randn(2*n,1);
c = randn(n,1);
d = randn;
cvx_begin
variable x(n)
dual variables y z
minimize( c' * x + d )
subject to
y : A * x <= b;
cvx_end
echo off
n = 10;
A = randn(2*n,n);
b = randn(2*n,1);
c = randn(n,1);
d = randn;
cvx_begin
variable x(n)
dual variables y z
minimize( c' * x + d )
subject to
y : A * x <= b;
cvx_end
Calling Mosek 9.1.9: 20 variables, 10 equality constraints
For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 10
Cones : 0
Scalar variables : 20
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 10
Cones : 0
Scalar variables : 20
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 10
Optimizer - Cones : 0
Optimizer - Scalar variables : 20 conic : 0
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 55 after factor : 55
Factor - dense dim. : 0 flops : 2.58e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.2e+01 8.9e+00 1.2e+01 0.00e+00 3.390345787e+00 0.000000000e+00 8.0e+00 0.00
1 1.5e+00 1.2e+00 1.7e+00 -7.79e-01 -2.769649874e+00 -2.917904931e+00 1.1e+00 0.01
2 4.2e-01 3.2e-01 4.5e-01 7.81e-01 -2.784207412e+00 -3.114199656e+00 2.9e-01 0.01
3 9.8e-02 7.6e-02 1.1e-01 1.28e+00 -1.097543070e+00 -1.178245652e+00 6.7e-02 0.01
4 5.0e-03 3.9e-03 5.4e-03 1.44e+00 -7.526682482e-01 -7.557845904e-01 3.4e-03 0.01
5 7.3e-04 5.7e-04 7.9e-04 1.01e+00 -7.519727476e-01 -7.524329845e-01 5.1e-04 0.01
6 8.2e-06 6.3e-06 8.8e-06 1.02e+00 -7.523030009e-01 -7.523084849e-01 5.6e-06 0.01
7 1.1e-09 8.4e-10 1.2e-09 1.00e+00 -7.522718552e-01 -7.522718558e-01 7.5e-10 0.01
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.00
Dual basis identification phase started.
Dual basis identification phase terminated. Time: 0.00
Basis identification terminated. Time: 0.00
Optimizer terminated. Time: 0.01
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -7.5227185516e-01 nrm: 2e+00 Viol. con: 2e-09 var: 0e+00
Dual. obj: -7.5227185582e-01 nrm: 1e+01 Viol. con: 0e+00 var: 4e-10
Basic solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -7.5227185171e-01 nrm: 2e+00 Viol. con: 8e-16 var: 0e+00
Dual. obj: -7.5227185582e-01 nrm: 1e+01 Viol. con: 0e+00 var: 2e-10
Optimizer summary
Optimizer - time: 0.01
Interior-point - iterations : 7 time: 0.01
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
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: Solved
Optimal value (cvx_optval): -0.188114
echo off