# Weighted analytic center of a set of linear inequalities

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    % 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