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Geometric branch-and-bound methods for constrained global optimization problems

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  • Daniel Scholz

Abstract

Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method using the concept of the rate of convergence in geometric branch-and-bound methods as introduced in some recent publications. Furthermore, some efficient further discarding tests using necessary conditions for optimality are derived and illustrated numerically on an obnoxious facility location problem. Copyright The Author(s) 2013

Suggested Citation

  • Daniel Scholz, 2013. "Geometric branch-and-bound methods for constrained global optimization problems," Journal of Global Optimization, Springer, vol. 57(3), pages 771-782, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:771-782
    DOI: 10.1007/s10898-012-9961-9
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    References listed on IDEAS

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    1. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    2. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
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    Cited by:

    1. Ana Rocha & M. Costa & Edite Fernandes, 2014. "A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues," Journal of Global Optimization, Springer, vol. 60(2), pages 239-263, October.

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