A Semidefinite Programming Approach to the Quadratic Knapsack Problem

C. Helmberg, F. Rendl and R. Weismantel
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C. Helmberg: Konrad Zuse Zentrum für Informationstechnik Berlin
F. Rendl: Technische Universität Graz, Institut für Mathematik
R. Weismantel: Universität Magdeburg, Institut für Mathematiche Optimierung

Journal of Combinatorial Optimization, 2000, vol. 4, issue 2, No 4, 197-215

Abstract: Abstract In order to gain insight into the quality of semidefinite relaxations of constrained quadratic 0/1 programming problems we study the quadratic knapsack problem. We investigate several basic semidefinite relaxations of this problem and compare their strength in theory and in practice. Various possibilities to improve these basic relaxations by cutting planes are discussed. The cutting planes either arise from quadratic representations of linear inequalities or from linear inequalities in the quadratic model. In particular, a large family of combinatorial cuts is introduced for the linear formulation of the knapsack problem in quadratic space. Computational results on a small class of practical problems illustrate the quality of these relaxations and cutting planes.

Keywords: semidefinite programming; quadratic knapsack problem; cutting planes; 0/1 polytopes; relaxations (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (16)

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DOI: 10.1023/A:1009898604624

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