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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. Riccardo Cambini, 2020. "Underestimation functions for a rank-two partitioning method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 465-489, December.
    2. 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.
    3. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    4. 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.
    5. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    6. Peter Dickinson, 2014. "On the exhaustivity of simplicial partitioning," Journal of Global Optimization, Springer, vol. 58(1), pages 189-203, January.
    7. Maranas, C. D. & Androulakis, I. P. & Floudas, C. A. & Berger, A. J. & Mulvey, J. M., 1997. "Solving long-term financial planning problems via global optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1405-1425, June.
    8. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    9. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, June.
    10. H. P. Benson, 2008. "Global Maximization of a Generalized Concave Multiplicative Function," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 105-120, April.
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