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: 88 variables, 42 equality constraints
------------------------------------------------------------
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 = 42, order n = 67, dim = 100, blocks = 23
nnz(A) = 95 + 0, nnz(ADA) = 524, nnz(L) = 283
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 8.13E+00 0.000
1 : 2.58E+00 2.64E+00 0.000 0.3241 0.9000 0.9000 2.56 1 1 2.2E+00
2 : 8.38E+00 8.62E-01 0.000 0.3269 0.9000 0.9000 0.76 1 1 9.5E-01
3 : 1.28E+01 2.95E-01 0.000 0.3429 0.9000 0.9000 0.64 1 1 3.8E-01
4 : 1.53E+01 9.65E-02 0.000 0.3267 0.9000 0.9000 0.81 1 1 1.4E-01
5 : 1.64E+01 1.78E-02 0.000 0.1841 0.9000 0.9000 0.95 1 1 2.5E-02
6 : 1.66E+01 2.57E-04 0.000 0.0145 0.0000 0.9000 1.00 1 1 1.5E-02
7 : 1.67E+01 1.54E-05 0.000 0.0597 0.9900 0.9582 1.00 1 1 9.2E-04
8 : 1.67E+01 5.24E-07 0.000 0.0341 0.9900 0.9438 1.00 1 1 3.7E-05
9 : 1.67E+01 1.29E-08 0.000 0.0246 0.9900 0.9828 1.00 1 1 9.1E-07
10 : 1.67E+01 5.64E-10 0.053 0.0439 0.9900 0.9900 1.00 1 1 4.0E-08
11 : 1.67E+01 2.82E-11 0.000 0.0499 0.9900 0.9900 1.00 2 2 2.0E-09
iter seconds digits c*x b*y
11 0.2 Inf 1.6683118800e+01 1.6683118802e+01
|Ax-b| = 1.7e-08, [Ay-c]_+ = 0.0E+00, |x|= 1.1e+01, |y|= 1.3e+01
Detailed timing (sec)
Pre IPM Post
1.000E-02 1.500E-01 1.000E-02
Max-norms: ||b||=3.848770e+00, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 3.83951.
------------------------------------------------------------
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!