Outer approximation for pseudo-convex mixed-integer nonlinear program problems

Outer approximation (OA) for solving convex mixed-integer nonlinear programming (MINLP) problems is heavily dependent on the convexity of functions and a natural issue is to relax the convexity assumption.This paper is devoted to OA for dealing with a pseudo-convex MINLP problem.By solving a sequence of nonlinear subproblems, we use Lagrange multiplier rules via Clarke subdifferentials of subproblems to introduce a parameter and then equivalently reformulate such MINLP as the mixed-integer linear program (MILP) master problem.Then, an OA algorithm is constructed to find the optimal solution to the MNILP by solving a sequence of MILP relaxations.The OA algorithm is proved to terminate after a finite number of steps.Numerical examples are illustrated to test the constructed OA algorithm.