涉及封闭集交集的稳健优化问题的最优性和对偶性

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-05-28 DOI:10.1007/s10957-024-02447-w

Nguyen Canh Hung, Thai Doan Chuong, Nguyen Le Hoang Anh

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引用次数: 0

摘要

本文研究了一个鲁棒优化问题，其约束条件包括非光滑和非凸函数以及闭集的交集。利用先进的变分分析工具，我们首先为稳健优化问题的最优性提供了必要条件。然后，我们在广义凸性假设下为所考虑问题的最优性建立了充分条件。此外，我们还提出了原始鲁棒优化问题的对偶问题，并研究了对偶关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

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Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.

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来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.