% JoÃ«lle Skaf - 04/24/08
%
% Consider the linear inequality constrained entroy maximization problem
%           maximize    -sum_{i=1}^n x_i*log(x_i)
%           subject to  sum(x) = 1
%                       Fx <= g
% where the variable is x \in \reals^{n}

% Input data
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);

% Entropy maximization
cvx_begin
variable x(n)
maximize sum(entr(x))
A*x == b
F*x <= g
cvx_end

% Results
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
-----------------------------------------------------------------
Cones  |             Errors              |
Mov/Act | Centering  Exp cone   Poly cone | Status
--------+---------------------------------+---------
20/ 20 | 1.695e+00  1.965e-01  3.726e-07 | Solved
20/ 20 | 7.851e-02  4.407e-04  1.906e-07 | Solved
16/ 20 | 2.624e-03  6.801e-07  1.779e-07 | Solved
0/ 20 | 3.861e-04  1.997e-07  1.811e-07 | Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +5.70335
The optimal solution is:
0.3445
0.3181
0.7540
0.8020
0.6418
0.3517
0.1982
0.2577
0.6372
0.3356
0.7109
0.8998
0.6086
0.6444
0.3060
0.4521
0.8885
0.7801
0.3106
0.6131