n = 2;
K = 11;
randn('state',0);
P = randn(n,K);
fprintf(1,'Minimizing the sum of the squares the distances to fixed points...');
cvx_begin
variable x(2)
minimize ( sum( square_pos( norms(x*ones(1,K) - P,2) ) ) )
cvx_end
fprintf(1,'Done! \n');
disp('------------------------------------------------------------------');
disp('The optimal point location is: ');
disp(x);
disp('The average location of the fixed points is');
disp(sum(P,2)/K);
disp('They are the same as expected!');
Minimizing the sum of the squares the distances to fixed points...
Calling Mosek 9.1.9: 88 variables, 42 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 : 42
Cones : 22
Scalar variables : 88
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 : 42
Cones : 22
Scalar variables : 88
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the dual
Optimizer - Constraints : 13
Optimizer - Cones : 22
Optimizer - Scalar variables : 66 conic : 66
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 : 36 after factor : 36
Factor - dense dim. : 0 flops : 3.57e+02
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.8e+00 1.0e+00 1.8e+01 0.00e+00 1.100000000e+01 -5.500000000e+00 1.0e+00 0.00
1 1.1e+00 2.7e-01 4.6e+00 -2.25e-01 9.166369810e+00 1.638467495e+00 2.7e-01 0.01
2 5.2e-01 1.4e-01 2.1e+00 1.36e-01 1.200674463e+01 7.093667824e+00 1.4e-01 0.01
3 1.0e-01 2.6e-02 2.2e-01 5.00e-01 1.516340210e+01 1.400919613e+01 2.6e-02 0.01
4 2.0e-02 5.2e-03 2.1e-02 8.19e-01 1.636949296e+01 1.612187949e+01 5.2e-03 0.01
5 1.5e-03 4.0e-04 4.5e-04 9.75e-01 1.665856181e+01 1.663945581e+01 4.0e-04 0.01
6 2.6e-05 6.7e-06 9.9e-07 9.99e-01 1.668267187e+01 1.668234611e+01 6.7e-06 0.01
7 1.6e-06 4.1e-07 1.5e-08 1.00e+00 1.668308885e+01 1.668306879e+01 4.1e-07 0.01
8 4.9e-08 1.3e-08 8.1e-11 1.00e+00 1.668311786e+01 1.668311725e+01 1.3e-08 0.01
9 1.7e-09 4.4e-10 5.2e-13 1.00e+00 1.668311882e+01 1.668311880e+01 4.4e-10 0.01
Optimizer terminated. Time: 0.01
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.6683118820e+01 nrm: 4e+00 Viol. con: 0e+00 var: 0e+00 cones: 4e-09
Dual. obj: 1.6683118799e+01 nrm: 7e+00 Viol. con: 0e+00 var: 3e-12 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): +16.6831
Done!
------------------------------------------------------------------
The optimal point location is:
0.0379
0.0785
The average location of the fixed points is
0.0379
0.0785
They are the same as expected!