Section 8.5.3: Analytic center of a set of linear inequalities
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;
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, sedumi is solving the dual problem.
sedumi will be called several times to refine the solution.
Original size: 155 variables, 60 equality constraints
50 exponentials add 400 variables, 250 equality constraints
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Errors
Act Centering Conic Status
-----------------------------------
50 2.900e+00 7.922e-01 Solved
50 1.949e-01 3.169e-03 Solved
50 1.162e-02 1.117e-05 Solved
50 1.492e-03 1.876e-07 Solved
50 1.792e-04 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
-1.1164
1.3141
1.2303
-0.0511
0.4031
0.1247