```% JoÃ«lle Skaf - 04/29/08
%
% The weighted analytic center of a set of linear inequalities:
%           a_i^Tx <= b_i   i=1,...,m,
% is the solution of the unconstrained minimization problem
%           minimize    -sum_{i=1}^m w_i*log(b_i-a_i^Tx),
% where w_i>0

% Input data
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);

% Analytic center
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.
sedumi will be called several times to refine the solution.
Original size: 160 variables, 100 equality constraints
50 exponentials add 400 variables, 250 equality constraints
-----------------------------------------------------------------
Cones  |             Errors              |
Mov/Act | Centering  Exp cone   Poly cone | Status
--------+---------------------------------+---------
50/ 50 | 2.579e+00  4.986e-01  6.898e-07 | Inaccurate/Solved
50/ 50 | 1.695e-01  2.052e-03  1.506e-07 | Solved
36/ 46 | 2.282e-02  3.118e-05  2.120e-07 | Solved
0/ 38 | 6.894e-04  2.432e-07  2.130e-07 | Solved
-----------------------------------------------------------------
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
0.2862
0.3779

```