randn('state', 0);
rand('state', 0);
n = 10;
m = 50;
p = 5;
tmp = randn(n,1);
A = randn(m,n);
b = A*tmp + 10*rand(m,1);
F = randn(p,n);
g = F*tmp;
cvx_begin
variable x(n)
minimize -sum(log(b-A*x))
F*x == g
cvx_end
disp(['The analytic center of the set of linear inequalities and ' ...
'equalities is: ']);
disp(x);
Calling Mosek 9.1.9: 155 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 : 155
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 : 155
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 10
Optimizer - Cones : 51
Optimizer - Scalar variables : 156 conic : 156
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 : 1.20e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.2e+00 5.1e+00 2.0e+02 0.00e+00 1.570825061e+02 -4.025510008e+01 1.0e+00 0.00
1 1.1e+00 1.8e+00 5.0e+01 2.26e-01 1.092238036e+02 2.053213161e+01 3.5e-01 0.01
2 5.3e-01 8.4e-01 1.8e+01 5.74e-01 8.996806321e+01 4.137705238e+01 1.7e-01 0.01
3 3.4e-01 5.4e-01 1.0e+01 7.24e-01 8.147598825e+01 4.781049976e+01 1.1e-01 0.01
4 1.6e-01 2.6e-01 3.4e+00 7.87e-01 7.302056894e+01 5.613860580e+01 5.1e-02 0.01
5 3.6e-02 5.8e-02 4.1e-01 8.40e-01 6.690306914e+01 6.275755062e+01 1.2e-02 0.01
6 8.8e-03 1.4e-02 5.2e-02 9.18e-01 6.533811840e+01 6.429369690e+01 2.8e-03 0.01
7 1.8e-03 2.8e-03 4.8e-03 9.81e-01 6.494959705e+01 6.473831929e+01 5.6e-04 0.01
8 1.6e-04 2.6e-04 1.4e-04 9.88e-01 6.485957897e+01 6.484001898e+01 5.1e-05 0.01
9 1.1e-05 1.7e-05 2.3e-06 9.98e-01 6.485101235e+01 6.484972020e+01 3.4e-06 0.01
10 1.1e-06 1.7e-06 7.5e-08 1.00e+00 6.485047018e+01 6.485033859e+01 3.4e-07 0.01
11 1.2e-07 1.8e-07 2.6e-09 1.00e+00 6.485041513e+01 6.485040111e+01 3.7e-08 0.01
12 1.7e-08 2.8e-08 1.5e-10 9.94e-01 6.485040940e+01 6.485040728e+01 5.8e-09 0.01
13 1.8e-08 2.5e-08 1.3e-10 1.00e+00 6.485040931e+01 6.485040739e+01 5.3e-09 0.01
14 1.5e-09 1.9e-09 2.8e-12 1.00e+00 6.485040864e+01 6.485040849e+01 4.1e-10 0.01
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 6.4850408639e+01 nrm: 2e+01 Viol. con: 6e-09 var: 0e+00 cones: 6e-10
Dual. obj: 6.4850408492e+01 nrm: 3e+00 Viol. con: 0e+00 var: 4e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 14 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): -64.8504
The analytic center of the set of linear inequalities and equalities is:
-0.3618
-1.5333
0.1387
0.2491
-1.1163
1.3142
1.2303
-0.0511
0.4031
0.1248