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Exact Solution Methods for the $k$-item Quadratic Knapsack Problem

Lucas Letocart(lucas.letocart***at***lipn.univ-paris13.fr)
Angelika Wiegele(angelika.wiegele***at***aau.at)

Abstract: The purpose of this paper is to solve the 0-1 k-item quadratic knapsack problem (kQKP), a problem of maximizing a quadratic function subject to two linear constraints.We propose an exact method based on semide nite optimization. The semide nite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.

Keywords: quadratic programming, 0-1 knapsack, k-cluster, semidefinite programming

Category 1: Combinatorial Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation:

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Entry Submitted: 03/08/2016
Entry Accepted: 03/08/2016
Entry Last Modified: 03/08/2016

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