echo on
n = 100;
A = randn(0.5*n,n);
b = randn(0.5*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;
z : x >= 0;
cvx_end
echo off
n = 100;
A = randn(0.5*n,n);
b = randn(0.5*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;
z : x >= 0;
cvx_end
Calling Mosek 9.1.9: 100 variables, 50 equality constraints
------------------------------------------------------------
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 : 50
Cones : 0
Scalar variables : 100
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 : 50
Cones : 0
Scalar variables : 100
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 50
Optimizer - Cones : 0
Optimizer - Scalar variables : 100 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 : 1275 after factor : 1275
Factor - dense dim. : 0 flops : 2.98e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.6e+01 1.1e+01 3.0e+01 0.00e+00 7.830148193e+00 0.000000000e+00 1.2e+01 0.00
1 6.4e+00 2.0e+00 5.4e+00 -7.05e-01 1.316749203e+00 -1.571374663e+00 2.1e+00 0.01
2 1.0e+00 3.1e-01 8.3e-01 -3.26e-01 -4.022147324e+00 -2.406022831e+00 3.3e-01 0.01
3 5.0e-03 1.5e-03 4.2e-03 -8.90e-01 -2.041272311e+03 5.898456059e-02 1.6e-03 0.01
4 5.0e-07 1.5e-07 4.2e-07 -9.99e-01 -2.031656979e+07 4.353189902e-02 1.6e-07 0.01
5 5.0e-11 1.5e-11 4.2e-11 -1.00e+00 -2.031657590e+11 4.353189854e-02 1.6e-11 0.01
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.00
Basis identification terminated. Time: 0.00
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.0000000000e+00 nrm: 2e+01 Viol. con: 1e-10 var: 0e+00
Basic solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -4.0468032652e+01 nrm: 2e+01 Viol. con: 1e-08 var: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 5 time: 0.01
Basis identification - time: 0.00
Primal - iterations : 49 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: Unbounded
Optimal value (cvx_optval): -Inf
echo off