Entropy maximization
randn('state', 0);
rand('state', 0);
n = 20;
m = 10;
p = 5;
tmp = rand(n,1);
A = randn(m,n);
b = A*tmp;
F = randn(p,n);
g = F*tmp + rand(p,1);
cvx_begin
variable x(n)
maximize sum(entr(x))
A*x == b
F*x <= g
cvx_end
display('The optimal solution is:' );
disp(x);
Successive approximation method to be employed.
sedumi will be called several times to refine the solution.
Original size: 65 variables, 35 equality constraints
20 exponentials add 160 variables, 100 equality constraints
-----------------------------------------------------------------
Errors
Act Centering Conic Status
-----------------------------------
20 1.496e+00 1.965e-01 Solved
20 7.829e-02 5.043e-04 Solved
20 8.273e-03 5.224e-06 Solved
20 1.036e-03 1.936e-07 Solved
20 1.297e-04 1.576e-07 Solved
20 1.629e-05 1.567e-07S Solved
20 1.673e-04S 3.731e-08 Solved
20 9.919e-05 8.009e-09 Solved
20 1.243e-05 7.994e-09S Solved
20 4.871e-05S 3.930e-10 Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +5.70335
The optimal solution is:
0.3445
0.3181
0.7539
0.8020
0.6418
0.3517
0.1981
0.2578
0.6373
0.3357
0.7109
0.8998
0.6085
0.6444
0.3061
0.4522
0.8886
0.7801
0.3106
0.6131