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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All the data used in Sect. 6 can be downloaded at https://github.com/hezhiluo/WCLO2022.
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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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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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DOI: https://doi.org/10.1007/s10898-023-01286-9