Section 7.1.1: Counting problems with Poisson distribution
rand('state',0);
n = 10;
m = 100;
atrue = rand(n,1);
btrue = rand;
u = rand(n,m);
mu = atrue'*u + btrue;
L = exp(-mu);
ns = ceil(max(10*mu));
y = sum(cumprod(rand(ns,m))>=L(ones(ns,1),:));
cvx_begin
variables a(n) b(1)
maximize sum(y.*log(a'*u+b) - (a'*u+b))
cvx_end
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: 276 variables, 103 equality constraints
92 exponentials add 736 variables, 460 equality constraints
-----------------------------------------------------------------
Errors
Act Centering Conic Status
-----------------------------------
92 6.171e-01 3.305e-02 Solved
92 8.713e-02 6.259e-04 Solved
92 1.348e-02 1.565e-05 Solved
92 1.754e-03 5.349e-07 Solved
92 2.200e-04 2.265e-07 Solved
92 2.791e-05 2.160e-07S Solved
92 3.407e-06 2.158e-07S Solved
92 3.030e-04S 2.188e-08 Solved
92 8.477e-05 3.812e-09 Solved
92 1.063e-05 3.362e-09 Solved
92 1.324e-06 3.389e-09S Solved
92 3.283e-06S 1.596e-09 Inaccurate/Solved
92 2.130e-05S 0.000e+00 Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +102.57