Separable Relaxation for Nonconvex Quadratic Integer Programming: Integer Diagonalization Approach

X. J. Zheng (), X. L. Sun () and D. Li ()
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X. J. Zheng: Shanghai University
X. L. Sun: Fudan University
D. Li: The Chinese University of Hong Kong

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 2, No 13, 463-489

Abstract: Abstract We present in this paper an integer diagonalization approach for deriving new lower bounds for general quadratic integer programming problems. More specifically, we introduce a semiunimodular transformation in order to diagonalize a symmetric matrix and preserve integral property of the feasible set at the same time. Via the semiunimodular transformation, the resulting separable quadratic integer program is a relaxation of the nonseparable quadratic integer program. We further define the integer diagonalization dual problem to identify the best semiunimodular transformation and analyze some basic properties of the set of semiunimodular transformations for a rational symmetric matrix. In particular, we present a complete characterization of the set of all semiunimodular transformations for a nonsingular 2×2 symmetric matrix. We finally discuss Lagrangian relaxation and convex relaxation schemes for the resulting separable quadratic integer programming problem and compare the tightness of different relaxation schemes.

Keywords: Quadratic integer programming; Separable relaxation; Semiunimodular congruence transformation; Lagrangian relaxation; Convex relaxation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-010-9653-x

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