n = 2;
K = 11;
randn('state',0);
P = randn(n,K);
fprintf(1,'Minimizing the L1-norm of the sum of the distances to fixed points...');
cvx_begin
variable x1(2)
minimize ( sum(norms(x1*ones(1,K) - P,1)) )
cvx_end
fprintf(1,'Done! \n');
fprintf(1,'Minimizing the L2-norm of the sum of the distances to fixed points...');
cvx_begin
variable x2(2)
minimize ( sum(norms(x2*ones(1,K) - P,2)) )
cvx_end
fprintf(1,'Done! \n');
disp('------------------------------------------------------------------');
disp('The optimal point location for the L1-norm case is: ');
disp(x1);
disp('The optimal point location for the L2-norm case is: ');
disp(x2);
Minimizing the L1-norm of the sum of the distances to fixed points...
Calling sedumi: 44 variables, 20 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 = 20, order n = 45, dim = 45, blocks = 1
nnz(A) = 80 + 0, nnz(ADA) = 200, nnz(L) = 110
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.17E+02 0.000
1 : 5.26E+00 3.27E+01 0.000 0.2803 0.9000 0.9000 2.72 1 1 9.7E-01
2 : 1.13E+01 6.73E+00 0.000 0.2058 0.9000 0.9000 1.18 1 1 3.0E-01
3 : 1.32E+01 1.58E+00 0.000 0.2347 0.9000 0.9000 1.02 1 1 8.0E-02
4 : 1.37E+01 3.53E-01 0.000 0.2235 0.9000 0.9000 1.00 1 1 1.9E-02
5 : 1.39E+01 1.98E-02 0.000 0.0561 0.9900 0.9900 1.00 1 1 1.1E-03
6 : 1.39E+01 5.68E-06 0.000 0.0003 0.9999 0.9999 1.00 1 1
iter seconds digits c*x b*y
6 0.0 Inf 1.3868099974e+01 1.3868099974e+01
|Ax-b| = 5.7e-16, [Ay-c]_+ = 0.0E+00, |x|= 4.1e+00, |y|= 4.2e+00
Detailed timing (sec)
Pre IPM Post
2.000E-02 4.000E-02 0.000E+00
Max-norms: ||b||=3.848770e+00, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +13.8681
Done!
Minimizing the L2-norm of the sum of the distances to fixed points...
Calling sedumi: 33 variables, 20 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 = 20, order n = 23, dim = 34, blocks = 12
nnz(A) = 40 + 0, nnz(ADA) = 400, nnz(L) = 210
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 3.51E+01 0.000
1 : 7.89E+00 9.87E+00 0.000 0.2808 0.9000 0.9000 2.94 1 1 8.2E-01
2 : 1.05E+01 2.03E+00 0.000 0.2060 0.9000 0.9000 1.12 1 1 1.8E-01
3 : 1.14E+01 1.65E-01 0.000 0.0812 0.9900 0.9900 1.01 1 1 1.5E-02
4 : 1.15E+01 1.04E-02 0.000 0.0631 0.9900 0.9900 1.00 1 1 9.7E-04
5 : 1.15E+01 9.90E-04 0.318 0.0950 0.9900 0.9900 1.00 1 1 9.4E-05
6 : 1.15E+01 1.90E-04 0.000 0.1918 0.9060 0.9000 1.00 1 1 1.8E-05
7 : 1.15E+01 3.42E-05 0.000 0.1802 0.9125 0.9000 1.00 1 1 3.1E-06
8 : 1.15E+01 5.45E-06 0.000 0.1592 0.9105 0.9000 1.00 1 1 5.2E-07
9 : 1.15E+01 8.33E-07 0.000 0.1529 0.9068 0.9000 1.00 1 1 8.8E-08
10 : 1.15E+01 5.77E-08 0.000 0.0693 0.9900 0.9900 1.00 2 2 6.9E-09
iter seconds digits c*x b*y
10 0.1 8.2 1.1483929331e+01 1.1483929255e+01
|Ax-b| = 1.3e-09, [Ay-c]_+ = 1.8E-09, |x|= 5.8e+00, |y|= 3.2e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 8.000E-02 0.000E+00
Max-norms: ||b||=3.848770e+00, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 8.90459.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +11.4839
Done!
------------------------------------------------------------------
The optimal point location for the L1-norm case is:
-0.0956
0.1139
The optimal point location for the L2-norm case is:
0.1251
0.1716