Journal of Global Optimization

, Volume 22, Issue 1, pp 17–37

Branch-and-bound approaches to standard quadratic optimization problems

Authors

  • Immanuel M. Bomze
    • Department of Statistics and Decision Support SystemsUniversity of Vienna
Article

DOI: 10.1023/A:1013886408463

Cite this article as:
Bomze, I.M. Journal of Global Optimization (2002) 22: 17. doi:10.1023/A:1013886408463

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.

D.C. decompositionSemidefinite relaxationReplicator dynamics
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© Kluwer Academic Publishers 2002