Solving a MINLP Optimization Problem

I have a mixed integer nonlinear optimization problem containing "log" function, and by the way it's convex if we relaxed the integer variables.

Can I solve it using Matlab Optimization toolbox efficiently or there will be some issues?

Is there a difference in solving such optimization problems if I used problem-based and used solver-based approaches?

Answer 1

[Alan Weiss]

There are two MINLP solvers in Global Optimization Toolbox: ga and surrogateopt. Either should work for you. The surrogateopt solver is primarily for time-consuming functions. Both solvers work best on relatively low-dimensional problems, up to 100 variables or so, but there are no built-in limits, so you can try larger problems.

There is also an example showing how intlinprog can sometimes be used iteratively to solve otherwise convex mixed-integer problems: Mixed-Integer Quadratic Programming Portfolio Optimization: Problem-Based or the nearly identical Mixed-Integer Quadratic Programming Portfolio Optimization: Solver-Based.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation