Branch-and-bound approaches to standard quadratic optimization problems

Authors:
Immanuel M. Bomze
Affiliations:
Department of Statistics and Decision Support Systems, University of Vienna, Vienna, Austria (E-mail: immanuel.bomze@univie.ac.at)
Venue:
Journal of Global Optimization
Year:
2002

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Abstract

This paper explores several possibilities for applying branch-and-bound techniques to a central problem class in quadratic programming, the so-called Standard Quadratic Problems (StQPs), which consist of finding a (global) minimizer of a quadratic form over the standard simplex. Since a crucial part of the procedures is based on efficient local optimization, different procedures to obtain local solutions are discussed, and a new class of ascent directions is proposed, for which a convergence result is established. Main emphasis is laid upon a d.c.-based branch-and-bound algorithm, and various strategies for obtaining an efficient d.c. decomposition are discussed.