无穷维变分分析中的变分凸性和强变分凸性

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-08-12 DOI:10.1137/23m1604667

P. D. Khanh, V. V. H. Khoa, B. S. Mordukhovich, V. T. Phat

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引用次数: 0

摘要

SIAM 优化期刊》第 34 卷第 3 期第 2756-2787 页，2024 年 9 月。摘要本文致力于系统研究低半连续函数的变凸性和强变凸性的基本概念及其特征。虽然这些概念是 Rockafellar 最近提出的，但它们的重要性在有限维变分分析和最优化中已经得到了认可和证明。在此，我们将讨论一般的无限维设置，并通过开发与有限维对应概念本质上不同的新技术，推导出变凸性和强变凸性概念的综合特征。根据所获得的特征，我们在巴拿赫空间的适当框架中建立了强变凸性与局部最小化的倾斜稳定性之间新的定量和定性关系。

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Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis

SIAM Journal on Optimization, Volume 34, Issue 3, Page 2756-2787, September 2024.
Abstract. This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by Rockafellar, the importance of them has already been recognized and documented in finite-dimensional variational analysis and optimization. Here we address general infinite-dimensional settings and derive comprehensive characterizations of both variational and strong variational convexity notions by developing novel techniques, which are essentially different from finite-dimensional counterparts. As a consequence of the obtained characterizations, we establish new quantitative and qualitative relationships between strong variational convexity and tilt stability of local minimizers in appropriate frameworks of Banach spaces.

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来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.