Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations

Research output: Contribution to journalArticlepeer-review

Abstract

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our rst formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we rst derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations signicantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.
Original languageEnglish
Number of pages40
JournalJournal of Global Optimization
Publication statusAccepted/In press - 19 Mar 2021

Fingerprint

Dive into the research topics of 'Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations'. Together they form a unique fingerprint.

Cite this