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: 68 variables (2 free), 44 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 2 free variables
eqs m = 44, order n = 49, dim = 82, blocks = 23
nnz(A) = 99 + 0, nnz(ADA) = 352, nnz(L) = 263
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 7.09E+000 0.000
1 : 5.29E+000 2.45E+000 0.000 0.3455 0.9000 0.9000 2.07 1 1 1.9E+000
2 : 1.13E+001 8.70E-001 0.000 0.3549 0.9000 0.9000 0.71 1 1 8.1E-001
3 : 1.50E+001 2.10E-001 0.000 0.2411 0.9000 0.9000 0.83 1 1 2.1E-001
4 : 1.65E+001 1.88E-002 0.000 0.0895 0.9900 0.9900 0.93 1 1 2.0E-002
5 : 1.67E+001 1.39E-003 0.000 0.0738 0.9900 0.9900 1.00 1 1 1.5E-003
6 : 1.67E+001 2.37E-005 0.000 0.0171 0.9900 0.9900 1.00 1 1 3.0E-005
7 : 1.67E+001 2.32E-008 0.406 0.0010 0.9900 0.9776 1.00 1 1 1.2E-006
8 : 1.67E+001 1.24E-009 0.106 0.0534 0.9900 0.9903 1.00 1 1 6.0E-008
9 : 1.67E+001 2.62E-010 0.000 0.2117 0.9000 0.8018 1.00 2 2 1.3E-008
iter seconds digits c*x b*y
9 0.1 Inf 1.6683118539e+001 1.6683118616e+001
|Ax-b| = 6.3e-008, [Ay-c]_+ = 1.1E-011, |x|= 1.3e+001, |y|= 1.4e+001
Detailed timing (sec)
Pre IPM Post
0.000E+000 6.009E-002 0.000E+000
Max-norms: ||b||=2.183186e+000, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.19573.
------------------------------------------------------------------------
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!