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Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound

Author

Listed:
  • Peiping Shen

    (North China University of Water Resources and Electric Power)

  • Dianxiao Wu

    (North China University of Water Resources and Electric Power)

  • Kaimin Wang

    (Henan Normal University)

Abstract

We consider in this paper a class of linear multiplicative programming problems that arise from numerous applications such as network flows and financial optimization. The problem is first transformed into an equivalent nonlinear optimization problem to provide a novel convex quadratic relaxation. A simplicial branch-and-bound algorithm is then designed to globally solve the problem, based on the proposed relaxation and simplicial branching process. The convergence and computational complexity of the algorithm are also analyzed. The results of numerical experiments confirm the efficiency of the proposed algorithm for tested instances.

Suggested Citation

  • Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:2:d:10.1007_s10898-023-01277-w
    DOI: 10.1007/s10898-023-01277-w
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    References listed on IDEAS

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    1. Cambini, Riccardo & Sodini, Claudio, 2010. "A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 25-29, November.
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    5. Riccardo Cambini & Claudio Sodini, 2010. "Global optimization of a rank-two nonconvex program," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 165-180, February.
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