I was trying to use cplex for matlab to solve my optimization problem. However, It seemed to me that cplex was only able to solve PURE integer programming problem with quadratic objective function and quadratic constraints. Well I can certainly use a fine grid to discretize my continuous parameters, but this is not my first option.
My questions are:
- Is this true? Or am I confused?
- If my impression was correct, is anybody aware of some reliable solver capable of doing so?
All the major commercial math programming solvers, including cplex and gurobi can solve mixed integer problems with convex quadratic objective functions. CPLEX has had that capability since 2007. They are as reliable as practically possible, but even linear mixed-integer programming is np-hard so it's possible to create small problems that can't solve with any solver. They perform much better than any grid search you could code in matlab.