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<h1>Weighted analytic center of a set of linear inequalities</h1>
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<pre class="codeinput">
<span class="comment">% Jo&Atilde;&laquo;lle Skaf - 04/29/08</span>
<span class="comment">%</span>
<span class="comment">% The weighted analytic center of a set of linear inequalities:</span>
<span class="comment">% a_i^Tx &lt;= b_i i=1,...,m,</span>
<span class="comment">% is the solution of the unconstrained minimization problem</span>
<span class="comment">% minimize -sum_{i=1}^m w_i*log(b_i-a_i^Tx),</span>
<span class="comment">% where w_i&gt;0</span>
<span class="comment">% Input data</span>
randn(<span class="string">'state'</span>, 0);
rand(<span class="string">'state'</span>, 0);
n = 10;
m = 50;
tmp = randn(n,1);
A = randn(m,n);
b = A*tmp + 2*rand(m,1);
w = rand(m,1);
<span class="comment">% Analytic center</span>
cvx_begin
variable <span class="string">x(n)</span>
minimize <span class="string">-sum(w.*log(b-A*x))</span>
cvx_end
disp(<span class="string">'The weighted analytic center of the set of linear inequalities is: '</span>);
disp(x);
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<pre class="codeoutput">
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
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