rand('state',1)
L = 20;
n = 10;
k = 7;
A = double(rand(L,n) <= k/L);
c = 0.9*rand(L,1)+0.1;
cvx_begin
variable x(n);
maximize(sum(log(x)))
subject to
A*x <= c
cvx_end
primal_obj = cvx_optval;
cvx_begin
variable lambda(L);
minimize(c'*lambda-sum(log(A'*lambda))-n)
subject to
lambda >= 0
cvx_end
dual_obj = cvx_optval;
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: 50 variables, 20 equality constraints
10 exponentials add 80 variables, 50 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
10/ 10 | 6.500e+00 2.563e+00 2.020e-06 | Solved
10/ 10 | 1.549e+00 1.764e-01 5.261e-07 | Solved
10/ 10 | 4.641e-02 1.530e-04 1.514e-07 | Solved
9/ 10 | 2.950e-03 6.398e-07 1.497e-07 | Solved
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -31.5685
Successive approximation method to be employed.
sedumi will be called several times to refine the solution.
Original size: 50 variables, 20 equality constraints
10 exponentials add 80 variables, 50 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
10/ 10 | 4.952e+00 1.547e+00 1.195e-07 | Solved
10/ 10 | 1.014e+00 7.468e-02 3.485e-07 | Solved
10/ 10 | 4.831e-02 1.652e-04 1.021e-07 | Solved
10/ 10 | 3.073e-03 6.930e-07 1.012e-07 | Solved
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -31.5685