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

Huixian Wu (), Hezhi Luo (), Xianye Zhang () and Haiqiang Qi ()
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Huixian Wu: Hangzhou Dianzi University
Hezhi Luo: Zhejiang Sci-Tech University
Xianye Zhang: Zhejiang Sci-Tech University
Haiqiang Qi: Zhejiang Sci-Tech University

Journal of Global Optimization, 2023, vol. 87, issue 1, No 6, 219 pages

Abstract: 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.

Keywords: Worst-case linear optimization; Successive convex optimization; Convex relaxation; Branch-and-bound; Computational complexity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01286-9

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