randn('seed',0);
n = 2;
m = 2*n;
A1 = randn(m,n);
b1 = randn(m,1);
A2 = randn(m,n);
b2 = randn(m,1);
fprintf(1,'Computing the distance between the 2 polyhedra...');
cvx_begin
variables x(n) y(n)
minimize (norm(x - y))
norm(x,1) <= 2;
norm(y-[4;3],inf) <=1;
cvx_end
fprintf(1,'Done! \n');
disp('------------------------------------------------------------------');
disp('The distance between the 2 polyhedra C and D is: ' );
disp(['dist(C,D) = ' num2str(cvx_optval)]);
disp('The optimal points are: ')
disp('x = '); disp(x);
disp('y = '); disp(y);
figure;
fill([-2; 0; 2; 0],[0;2;0;-2],'b', [3;5;5;3],[2;2;4;4],'r')
axis([-3 6 -3 6])
axis square
hold on;
plot(x(1),x(2),'k.')
plot(y(1),y(2),'k.')
plot([x(1) y(1)],[x(2) y(2)])
title('Euclidean distance between 2 polyhedron in R^2');
xlabel('x_1');
ylabel('x_2');
Computing the distance between the 2 polyhedra...
Calling Mosek 9.1.9: 15 variables, 5 equality constraints
------------------------------------------------------------
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 : 5
Cones : 5
Scalar variables : 15
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 : 5
Cones : 5
Scalar variables : 15
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 3
Optimizer - Cones : 3
Optimizer - Scalar variables : 10 conic : 7
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 : 6 after factor : 6
Factor - dense dim. : 0 flops : 5.40e+01
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.0e+00 1.0e+00 2.0e+00 0.00e+00 1.000000000e+00 0.000000000e+00 1.0e+00 0.00
1 1.6e+00 3.9e-01 7.4e-01 -7.69e-02 1.745839661e+00 1.452430446e+00 3.9e-01 0.02
2 4.4e-01 1.1e-01 9.0e-02 9.65e-01 2.438967963e+00 2.285065173e+00 1.1e-01 0.02
3 4.9e-02 1.2e-02 3.6e-03 9.07e-01 2.134713080e+00 2.118964344e+00 1.2e-02 0.02
4 3.7e-04 9.4e-05 2.4e-06 9.88e-01 2.121484330e+00 2.121364392e+00 9.4e-05 0.02
5 2.2e-05 5.5e-06 3.4e-08 1.00e+00 2.121333459e+00 2.121326455e+00 5.5e-06 0.02
6 1.1e-06 2.7e-07 3.6e-10 1.00e+00 2.121321075e+00 2.121320737e+00 2.7e-07 0.02
7 2.1e-08 5.2e-09 1.0e-12 1.00e+00 2.121320359e+00 2.121320352e+00 5.2e-09 0.02
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 2.1213203591e+00 nrm: 4e+00 Viol. con: 8e-13 var: 0e+00 cones: 1e-08
Dual. obj: 2.1213203524e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 cones: 4e-09
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 7 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): +2.12132
Done!
------------------------------------------------------------------
The distance between the 2 polyhedra C and D is:
dist(C,D) = 2.1213
The optimal points are:
x =
1.5000
0.5000
y =
3.0000
2.0000
