约束优化问题中最小值的稳定性和隐函数定理

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-05-29 DOI:10.1007/s10957-024-02459-6

Aram V. Arutyunov, Kirill A. Tsarkov, Sergey E. Zhukovskiy

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引用次数: 0

摘要

在本文中，我们考虑了具有包含型和相等型约束的有限维和无限维优化问题。我们获得了该问题的解在弱拓扑结构中相对于问题参数的小扰动具有稳定性的充分条件。在有限维情况下，我们还获得了带有相等类型约束条件的问题的强拓扑解的稳定性条件。这些条件基于某个隐函数定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem

In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology of the solution are obtained for the problem with equality-type constraints. These conditions are based on a certain implicit function theorem.

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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.