randn('state',0);
n = 10; m = 2*n;
A = randn(m,n);
b = A*rand(n,1) + 2*rand(m,1);
norm_ai = sum(A.^2,2).^(.5);
fprintf(1,'Computing Chebyshev center...');
cvx_begin
variable r(1)
variable x_c(n)
dual variable y
maximize ( r )
y: A*x_c + r*norm_ai <= b;
cvx_end
fprintf(1,'Done! \n');
fprintf(1,'The Chebyshev center coordinates are: \n');
disp(x_c);
fprintf(1,'The radius of the largest Euclidean ball is: \n');
disp(r);
Computing Chebyshev center...
Calling Mosek 9.1.9: 20 variables, 11 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 : 11
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 : 11
Cones : 0
Scalar variables : 20
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 11
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 : 66 after factor : 66
Factor - dense dim. : 0 flops : 3.15e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.1e+01 4.7e+00 4.2e+01 0.00e+00 1.800847484e+01 0.000000000e+00 4.8e+00 0.00
1 1.1e+00 1.7e-01 1.5e+00 -2.05e-01 8.329859321e-01 -1.351392910e-01 1.7e-01 0.01
2 2.3e-01 3.4e-02 3.1e-01 8.87e-01 4.003042853e-01 2.086959117e-01 3.5e-02 0.01
3 7.0e-02 1.1e-02 9.4e-02 7.24e-01 3.291684363e-01 2.681986266e-01 1.1e-02 0.01
4 1.4e-02 8.3e-04 1.2e-02 7.64e-01 3.127686118e-01 3.004715227e-01 1.9e-03 0.01
5 5.5e-03 3.3e-04 4.7e-03 -1.84e-01 3.243044563e-01 3.181611000e-01 7.3e-04 0.01
6 1.3e-03 7.8e-05 1.1e-03 7.76e-01 3.341258689e-01 3.326409576e-01 1.7e-04 0.01
7 8.5e-05 5.0e-06 7.2e-05 1.02e+00 3.368651344e-01 3.367873239e-01 1.1e-05 0.01
8 6.1e-07 3.6e-08 5.1e-07 1.00e+00 3.370587443e-01 3.370581838e-01 8.0e-08 0.01
9 6.1e-11 3.6e-12 5.2e-11 1.00e+00 3.370593981e-01 3.370593981e-01 8.0e-12 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: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.3705939813e-01 nrm: 1e+00 Viol. con: 3e-10 var: 0e+00
Dual. obj: 3.3705939807e-01 nrm: 1e+01 Viol. con: 0e+00 var: 4e-12
Basic solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.3705939820e-01 nrm: 1e+00 Viol. con: 2e-16 var: 0e+00
Dual. obj: 3.3705939807e-01 nrm: 1e+01 Viol. con: 0e+00 var: 2e-15
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 9 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): +0.337059
Done!
The Chebyshev center coordinates are:
-0.1116
-1.5760
0.1079
-2.1751
3.2264
3.5820
4.3394
3.0680
0.4449
0.3164
The radius of the largest Euclidean ball is:
0.3371