Weighted analytic center of a set of linear inequalities
randn('state', 0);
rand('state', 0);
n = 10;
m = 50;
tmp = randn(n,1);
A = randn(m,n);
b = A*tmp + 2*rand(m,1);
w = rand(m,1);
cvx_begin
variable x(n)
minimize -sum(w.*log(b-A*x))
cvx_end
disp('The weighted analytic center of the set of linear inequalities is: ');
disp(x);
Successive approximation method to be employed.
For improved efficiency, sedumi is solving the dual problem.
sedumi will be called several times to refine the solution.
Original size: 150 variables, 60 equality constraints
50 exponentials add 400 variables, 250 equality constraints
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Errors
Act Centering Conic Status
-----------------------------------
50 3.534e+00 1.215e+00 Solved
50 3.015e-01 7.641e-03 Solved
50 1.751e-02 2.422e-05 Solved
50 2.259e-03 6.714e-07 Solved
50 2.831e-04 4.010e-07 Solved
50 3.706e-04S 1.109e-08 Solved
50 6.259e-05 0.000e+00 Solved
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Status: Solved
Optimal value (cvx_optval): +5.99254
The weighted analytic center of the set of linear inequalities is:
-0.5100
-1.4794
0.3397
0.1944
-1.0444
1.1956
1.3927
-0.2815
0.2863
0.3779