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A geometric branch and bound method for robust maximization of convex functions

Author

Listed:
  • Fengqiao Luo

    (Northwestern University)

  • Sanjay Mehrotra

    (Northwestern University)

Abstract

We investigate robust optimization problems defined for maximizing convex functions. While the problems arise in situations which are naturally modeled as minimization of concave functions, they also arise when a decision maker takes an optimistic approach to making decisions with convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm performs sequential piecewise-linear approximations of the convex objective, and solves linear programs to determine lower and upper bounds at each node. Finite convergence of the algorithm to an $$\epsilon -$$ ϵ - optimal solution is proved. Numerical results are used to discuss the performance of the developed algorithm. The algorithm developed in this paper can be used as an oracle in the cutting surface method for solving robust optimization problems with compact ambiguity sets.

Suggested Citation

  • Fengqiao Luo & Sanjay Mehrotra, 2021. "A geometric branch and bound method for robust maximization of convex functions," Journal of Global Optimization, Springer, vol. 81(4), pages 835-859, December.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:4:d:10.1007_s10898-021-01038-7
    DOI: 10.1007/s10898-021-01038-7
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    References listed on IDEAS

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    1. Yongzhen Li & Jia Shu & Miao Song & Jiawei Zhang & Huan Zheng, 2017. "Multisourcing Supply Network Design: Two-Stage Chance-Constrained Model, Tractable Approximations, and Computational Results," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 287-300, May.
    2. Zuo-Jun Max Shen & Collette Coullard & Mark S. Daskin, 2003. "A Joint Location-Inventory Model," Transportation Science, INFORMS, vol. 37(1), pages 40-55, February.
    3. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    4. Lakshman S. Thakur, 1991. "Domain Contraction in Nonlinear Programming: Minimizing a Quadratic Concave Objective Over a Polyhedron," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 390-407, May.
    5. Benson, Harold P., 2007. "A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 597-611, October.
    6. D. Gerard & M. Köppe & Q. Louveaux, 2017. "Guided dive for the spatial branch-and-bound," Journal of Global Optimization, Springer, vol. 68(4), pages 685-711, August.
    7. Benson, Harold P., 2006. "Fractional programming with convex quadratic forms and functions," European Journal of Operational Research, Elsevier, vol. 173(2), pages 351-369, September.
    8. Peter Kirst & Oliver Stein & Paul Steuermann, 2015. "Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 591-616, July.
    9. H. P. Benson, 2007. "Solving Sum of Ratios Fractional Programs via Concave Minimization," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 1-17, October.
    Full references (including those not matched with items on IDEAS)

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