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.
SDPT3 will be called several times to refine the solution.
Original size: 276 variables, 103 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
Approximation size: 1013 variables, 563 equality constraints
-----------------------------------------------------------------
Target Conic Solver
Precision Error Status
---------------------------
1.221e-04 3.273e-02 Solved
1.221e-04 5.765e-04 Solved
1.221e-04 0.000e+00 Solved
1.490e-08 1.031e-06 Solved
1.490e-08 0.000e+00 Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +102.57