Appropriate solver for integer programming and log function


I am trying to solve an optimization problem that has integer variables and log functions. The problem is similar to the following:


variable p(2) r

variable x(2) binary

maximize r

subject to

   r <= sum(log (1 + p)) ;
   p <= 2 * x ;
   sum(x) <= 1;


Apart from the binary integer variables, the problem is concave. I wonder which solver (Gurobi, Mosek, GLPK) can solve this? I am asking since I will have to download these licenses separately to solve my mixed integer non-linear programs.



You will not be able to solve problems of this type with CVX, unfortunately. CVX cannot handle both logarithmic functions and binary/integer variables at the same time. This is due to the heuristic approach that CVX must take in order to implement the logarithm function.

Thanks for the reply. Do you know of any other solver/toolbox that can handle both log function and integer variables? Due to the nature of my optimization problem, I cannot escape from these two characteristics :S

I do not, I am sorry.