randn('state', 0);
rand('state', 0);
n = 10;
m = 50;
tmp = randn(n,1);
A = randn(m,n);
b = A*tmp + 2*rand(m,1);
w = rand(m,1);
cvx_begin
variable x(n)
minimize -sum(w.*log(b-A*x))
cvx_end
disp('The weighted analytic center of the set of linear inequalities is: ');
disp(x);
Calling Mosek 9.1.9: 150 variables, 60 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 : 60
Cones : 50
Scalar variables : 150
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 : 60
Cones : 50
Scalar variables : 150
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 10
Optimizer - Cones : 50
Optimizer - Scalar variables : 150 conic : 150
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 : 1.14e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 5.8e+00 3.2e+00 8.3e+01 0.00e+00 6.028258137e+01 -2.204216600e+01 1.0e+00 0.00
1 1.9e+00 1.0e+00 1.8e+01 6.36e-01 2.402764877e+01 -7.490705411e+00 3.3e-01 0.01
2 6.6e-01 3.6e-01 4.1e+00 7.86e-01 7.484274349e+00 -4.700807210e+00 1.1e-01 0.01
3 4.0e-01 2.2e-01 2.0e+00 8.15e-01 2.978822508e+00 -4.803366948e+00 6.8e-02 0.01
4 1.5e-01 8.2e-02 5.3e-01 7.16e-01 -2.181211154e+00 -5.559357961e+00 2.6e-02 0.01
5 4.9e-02 2.7e-02 1.1e-01 8.18e-01 -4.601865218e+00 -5.810948806e+00 8.5e-03 0.01
6 1.1e-02 6.0e-03 1.2e-02 8.75e-01 -5.671320321e+00 -5.959202164e+00 1.9e-03 0.01
7 1.8e-03 9.9e-04 8.3e-04 9.69e-01 -5.937967101e+00 -5.985922606e+00 3.1e-04 0.01
8 3.2e-05 1.7e-05 2.0e-06 9.89e-01 -5.991594363e+00 -5.992445856e+00 5.5e-06 0.01
9 1.1e-06 6.0e-07 1.3e-08 9.99e-01 -5.992505691e+00 -5.992535031e+00 1.9e-07 0.01
10 1.2e-07 6.1e-08 4.2e-10 1.00e+00 -5.992537162e+00 -5.992540134e+00 1.9e-08 0.01
11 4.1e-08 9.9e-09 2.8e-11 1.01e+00 -5.992540319e+00 -5.992540801e+00 3.3e-09 0.01
12 2.9e-08 1.5e-09 1.6e-12 1.02e+00 -5.992540760e+00 -5.992540832e+00 5.0e-10 0.01
13 2.9e-08 1.5e-09 1.6e-12 1.00e+00 -5.992540760e+00 -5.992540832e+00 5.0e-10 0.02
14 2.9e-08 1.5e-09 1.6e-12 1.00e+00 -5.992540760e+00 -5.992540832e+00 5.0e-10 0.02
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -5.9925407602e+00 nrm: 2e+01 Viol. con: 5e-08 var: 0e+00 cones: 7e-10
Dual. obj: -5.9925408321e+00 nrm: 3e+00 Viol. con: 0e+00 var: 1e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 15 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): +5.99254
The weighted analytic center of the set of linear inequalities is:
-0.5100
-1.4794
0.3397
0.1944
-1.0444
1.1956
1.3927
-0.2815
0.2863
0.3779