randn('state',0);
rand('state',0);
n = 5;
m1 = 2*n;
m2 = 3*n;
A1 = randn(m1,n);
A2 = randn(m2,n);
b1 = rand(m1,1);
b2 = rand(m2,1) + A2*randn(n,1);
cvx_begin
variables x(n) y(n)
minimize (norm(x - y))
A1*x <= b1;
A2*y <= b2;
cvx_end
disp('------------------------------------------------------------------');
disp('The distance between the 2 polyhedra C and D is: ' );
disp(['dist(C,D) = ' num2str(cvx_optval)]);
Calling Mosek 9.1.9: 31 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 : CONIC (conic optimization problem)
Constraints : 11
Cones : 1
Scalar variables : 31
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 : 11
Cones : 1
Scalar variables : 31
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 10
Optimizer - Cones : 1
Optimizer - Scalar variables : 31 conic : 6
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 : 1.28e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 2.8e+00 2.0e+00 0.00e+00 0.000000000e+00 -1.000000000e+00 1.0e+00 0.00
1 6.0e-01 1.7e+00 9.5e-01 9.82e-01 -8.785174286e-01 -1.470841345e+00 6.0e-01 0.01
2 9.6e-02 2.7e-01 5.4e-02 1.29e+00 -9.869558390e-01 -1.077814479e+00 9.6e-02 0.01
3 3.2e-02 9.1e-02 1.1e-02 9.09e-01 -6.203091476e-01 -6.506016222e-01 3.2e-02 0.01
4 6.7e-03 1.9e-02 9.7e-04 1.07e+00 -5.209512788e-01 -5.277022343e-01 6.7e-03 0.01
5 7.1e-04 2.0e-03 3.3e-05 1.02e+00 -5.096057183e-01 -5.103276429e-01 7.1e-04 0.01
6 6.1e-06 1.7e-05 2.6e-08 1.00e+00 -5.085792095e-01 -5.085854747e-01 6.1e-06 0.01
7 5.9e-07 1.7e-06 7.8e-10 1.00e+00 -5.085684859e-01 -5.085690923e-01 5.9e-07 0.01
8 5.6e-08 1.6e-07 2.3e-11 1.00e+00 -5.085672068e-01 -5.085672644e-01 5.6e-08 0.01
9 2.1e-09 6.0e-09 1.7e-13 1.00e+00 -5.085670657e-01 -5.085670679e-01 2.1e-09 0.01
Optimizer terminated. Time: 0.01
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -5.0856706572e-01 nrm: 1e+00 Viol. con: 3e-13 var: 2e-09 cones: 0e+00
Dual. obj: -5.0856706791e-01 nrm: 2e+00 Viol. con: 0e+00 var: 5e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.01
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): +0.508567
------------------------------------------------------------------
The distance between the 2 polyhedra C and D is:
dist(C,D) = 0.50857