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);
CVX Warning:
Models involving "log" or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
The method requires multiple calls to the solver, so it can be slow; and
in certain cases it fails to converge. See Appendix D of the the user's
guide for more information about this method, and for instructions on how
to suppress this warning in the future.
Successive approximation method to be employed.
sedumi will be called several times to refine the solution.
Original size: 160 variables, 105 equality constraints
50 exponentials add 400 variables, 250 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
50/ 50 | 2.303e+00 3.573e-01 5.090e-08 | Solved
49/ 50 | 1.788e-01 2.265e-03 2.233e-07 | Solved
30/ 50 | 1.486e-02 1.622e-05 2.066e-07 | Solved
0/ 50 | 8.671e-04 2.138e-07 2.038e-07 | 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
0.4030
0.1248