Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Pierre Bonami (1) , Mustafa Kilinç (2) , Jeff Linderoth (2)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
2 ISyE - Department of Industrial and Systems Engineering [Wisconsin-Madison]

This paper provides a survey of recent progress and software for solving mixed integer nonlinear programs (MINLP) wherein the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in very years. By exploiting analogies to the case of well-known techniques for solving mixed integer linear programs and incorporating these techniques into the software, significant improvements have been made in our ability to solve the problems.

Mots clés: Mixed Integer Nonlinear Programming; Branch and Bound

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Pierre Bonami, Mustafa Kilinç, Jeff Linderoth. Algorithms and Software for Convex Mixed Integer Nonlinear Programs. 2009. ⟨hal-00423416v2⟩