FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs

We describe a new solver for convex mixed-integer nonlinear programs (MINLPs) that implements a linearization-based algorithm. The solver is based on an algorithm of Quesada and Grossmann [Quesada, I., I. E. Grossmann. 1992. An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems. Comput. Chemical Engrg.16(10--11) 937--947] that avoids the complete re-solution of a master mixed-integer linear program (MILP) by adding new linearizations at open nodes of the branch-and-bound tree whenever an integer solution is found. The new solver, FilMINT, combines the MINTO branch-and-cut framework for MILP with filterSQP to solve the nonlinear programs that arise as subproblems in the algorithm. The MINTO framework allows us to easily employ cutting planes, primal heuristics, and other well-known MILP enhancements for MINLPs. We present detailed computational experiments that show the benefit of such advanced MILP techniques. We offer new suggestions for generating and managing linearizations that are shown to be efficient on a wide range of MINLPs. By carefully incorporating and tuning all these enhancements, an effective solver for convex MINLPs is constructed.