```% Boyd & Vandenberghe "Convex Optimization"
% JoÃ«lle Skaf - 04/29/08
%
% The analytic center of a set of linear inequalities and equalities:
%           a_i^Tx <= b_i   i=1,...,m,
%           Fx = g,
% is the solution of the unconstrained minimization problem
%           minimize    -sum_{i=1}^m log(b_i-a_i^Tx).

% Input data
randn('state', 0);
rand('state', 0);
n = 10;
m = 50;
p = 5;
tmp = randn(n,1);
A = randn(m,n);
b = A*tmp + 10*rand(m,1);
F = randn(p,n);
g = F*tmp;

% Analytic center
cvx_begin
variable x(n)
minimize -sum(log(b-A*x))
F*x == g
cvx_end

disp(['The analytic center of the set of linear inequalities and ' ...
'equalities is: ']);
disp(x);
```
```
Successive approximation method to be employed.
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 155 variables, 60 equality constraints
50 exponentials add 400 variables, 250 equality constraints
-----------------------------------------------------------------
Cones  |             Errors              |
Mov/Act | Centering  Exp cone   Poly cone | Status
--------+---------------------------------+---------
50/ 50 | 3.700e+00  7.922e-01  0.000e+00 | Solved
50/ 50 | 6.027e-01  2.364e-02  0.000e+00 | Solved
46/ 50 | 5.799e-02  2.176e-04  0.000e+00 | Solved
13/ 39 | 6.785e-03  2.986e-06  0.000e+00 | Solved
2/ 12 | 7.432e-04  3.537e-08  0.000e+00 | Solved
0/  1 | 8.438e-05  6.251e-11  0.000e+00 | Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -64.8504

The analytic center of the set of linear inequalities and equalities is:
-0.3618
-1.5333
0.1387
0.2491
-1.1163
1.3142
1.2303
-0.0511
0.4031
0.1248

```