echo on
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable x(n)
minimize( norm( A*x-b ) )
cvx_end
echo off
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable x(n)
minimize( norm( A*x-b ) )
cvx_end
Calling Mosek 9.1.9: 201 variables, 101 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 : CONIC (conic optimization problem)
Constraints : 101
Cones : 1
Scalar variables : 201
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 : CONIC (conic optimization problem)
Constraints : 101
Cones : 1
Scalar variables : 201
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 100
Optimizer - Cones : 1
Optimizer - Scalar variables : 201 conic : 201
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 : 5050 after factor : 5050
Factor - dense dim. : 0 flops : 2.37e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 0.0e+00 2.5e+00 2.0e+00 0.00e+00 0.000000000e+00 -1.000000000e+00 1.0e+00 0.01
1 1.0e-14 2.0e-01 2.4e-01 -9.59e-01 -7.817372397e+00 -6.384277430e+00 8.0e-02 0.02
2 1.7e-15 1.8e-03 1.7e-04 5.88e-01 -9.702996479e+00 -9.697506233e+00 7.2e-04 0.02
3 9.7e-12 9.5e-11 1.1e-15 9.95e-01 -9.734018206e+00 -9.734018207e+00 1.8e-12 0.02
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -9.7340182062e+00 nrm: 1e+00 Viol. con: 1e-15 var: 0e+00 cones: 0e+00
Dual. obj: -9.7340182072e+00 nrm: 1e+01 Viol. con: 0e+00 var: 1e-10 cones: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 3 time: 0.02
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): +9.73402
echo off