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

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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 \(\epsilon \)-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.

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Availability of data and materials

All the data used in Sect. 6 can be downloaded at https://github.com/hezhiluo/WCLO2022.

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Acknowledgements

The authors would like to thank the Associate Editor and the two anonymous referees for the detailed comments and valuable suggestions, which have improved the final presentation of the paper.

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  1. Department of Mathematics, College of Science, Hangzhou Dianzi University, 310018, Hangzhou, Zhejiang, China

    Huixian Wu

  2. Department of Mathematics, College of Science, Zhejiang Sci-Tech University, 310018, Hangzhou, Zhejiang, China

    Hezhi Luo, Xianye Zhang & Haiqiang Qi

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  1. Huixian Wu
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Correspondence to Hezhi Luo.

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This work is jointly supported by the National Natural Science Foundation of China (NSFC) [Grants 12271485, 11871433 and U22A2004] and the Zhejiang Provincial NSFC [Grant LZ21A010003].

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Wu, H., Luo, H., Zhang, X. et al. An effective global algorithm for worst-case linear optimization under polyhedral uncertainty. J Glob Optim 87, 191–219 (2023). https://doi.org/10.1007/s10898-023-01286-9

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