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An effective global algorithm for worst-case linear optimization under polyhedral uncertainty

Author

Listed:
  • Huixian Wu

    (Hangzhou Dianzi University)

  • Hezhi Luo

    (Zhejiang Sci-Tech University)

  • Xianye Zhang

    (Zhejiang Sci-Tech University)

  • Haiqiang Qi

    (Zhejiang Sci-Tech University)

Abstract

In this paper, we investigate effective algorithms for the worst-case linear optimization (WCLO) under polyhedral uncertainty on the right-hand-side of the constraints that arises from a broad range of applications and is known to be strongly NP-hard. We first develop a successive convex optimization (SCO) algorithm for WCLO and show that it converges to a local solution of the transformed problem of WCLO. Second, we develop a global algorithm (called SCOBB) for WCLO that finds a globally optimal solution to the underlying WCLO within a pre-specified $$\epsilon $$ ϵ -tolerance by integrating the SCO method, LO relaxation, branch-and-bound framework and initialization. We establish the global convergence of the SCOBB algorithm and estimate its complexity. Finally, we integrate the SCOBB algorithm for WCLO to develop a global algorithm for the two-stage adaptive robust optimization with a polyhedral uncertainty set. Preliminary numerical results illustrate that the SCOBB algorithm can effectively find a global optimal solution to medium and large-scale WCLO instances.

Suggested Citation

  • Huixian Wu & Hezhi Luo & Xianye Zhang & Haiqiang Qi, 2023. "An effective global algorithm for worst-case linear optimization under polyhedral uncertainty," Journal of Global Optimization, Springer, vol. 87(1), pages 191-219, September.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:1:d:10.1007_s10898-023-01286-9
    DOI: 10.1007/s10898-023-01286-9
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    References listed on IDEAS

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