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On the resolution of certain discrete univariate max–min problems

Rangarajan, Ramsharan (2017) On the resolution of certain discrete univariate max–min problems. In: Computational Optimization and Applications, 68 (1). pp. 163-192. ISSN 0926-6003

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Official URL: https://doi.org/10.1007/s10589-017-9903-z


We analyze a class of discrete, univariate, and strictly quasiconcave max–min problems. A distinctive feature of max–min-type optimization problems is the nonsmoothness of the objective being maximized. Here we exploit strict quasiconcavity of the given set of functions to prove existence and uniqueness of the optimizer, and to provide computable bounds for it. The analysis inspires an efficient algorithm for computing the optimizer without having to resort to any regularization or heuristics. We prove correctness of the proposed algorithm and briefly discuss the effect of tolerances and approximate computation. Our study finds direct application in the context of certain mesh deformation methods, wherein the optimal perturbation for a vertex is computed as the solution of a max–min problem of the type we consider here. We include examples demonstrating improvement of simplicial meshes while adopting the proposed algorithm for resolution of the optimization problems involved, and use these numerical experiments to examine the performance of the algorithm.

Item Type: Journal Article
Publication: Computational Optimization and Applications
Publisher: Springer New York LLC
Additional Information: The copyright of this article belongs to the Springer New York LLC.
Keywords: Discrete minimax; Mesh optimization; Mesh smoothing; Nonsmooth optimization; Polynomial roots; Quasiconvex optimization
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 26 May 2022 09:15
Last Modified: 26 May 2022 09:15
URI: https://eprints.iisc.ac.in/id/eprint/72687

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