One free point localization
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 sedumi: 77 variables, 35 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 35, order n = 56, dim = 89, blocks = 23
nnz(A) = 77 + 0, nnz(ADA) = 169, nnz(L) = 102
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.57E+00 0.000
1 : -1.55E+00 8.66E-01 0.000 0.3370 0.9000 0.9000 2.56 1 1 2.2E+00
2 : -7.67E+00 3.21E-01 0.000 0.3707 0.9000 0.9000 0.75 1 1 6.2E-01
3 : -1.28E+01 1.00E-01 0.000 0.3130 0.9000 0.9000 0.71 1 1 2.1E-01
4 : -1.54E+01 2.95E-02 0.000 0.2932 0.9000 0.9000 0.84 1 1 6.7E-02
5 : -1.66E+01 2.43E-03 0.000 0.0825 0.9900 0.9900 0.95 1 1 5.7E-03
6 : -1.66E+01 3.46E-05 0.293 0.0142 0.9000 0.0000 1.00 1 1 3.4E-03
7 : -1.66E+01 6.13E-06 0.000 0.1773 0.9151 0.9000 1.00 1 1 6.6E-04
8 : -1.67E+01 4.35E-08 0.161 0.0071 0.9990 0.9990 1.00 1 1 4.4E-06
9 : -1.67E+01 1.09E-08 0.093 0.2512 0.8840 0.9000 1.00 1 1 1.1E-06
10 : -1.67E+01 1.86E-09 0.028 0.1700 0.0000 0.9000 1.00 1 1 2.4E-07
11 : -1.67E+01 1.49E-10 0.000 0.0801 0.9900 0.9511 1.00 1 1 2.0E-08
12 : -1.67E+01 1.17E-11 0.309 0.0787 0.9900 0.9900 1.00 2 2 1.6E-09
iter seconds digits c*x b*y
12 0.1 Inf -1.6683118749e+01 -1.6683118746e+01
|Ax-b| = 6.7e-10, [Ay-c]_+ = 3.1E-09, |x|= 1.7e+01, |y|= 8.3e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 7.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 3.848770e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 4.39187.
------------------------------------------------------------
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!