一般优化问题的顺序 M 静态条件

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED Set-Valued and Variational Analysis Pub Date : 2024-06-19 DOI:10.1007/s11228-024-00724-4

Nooshin Movahedian, Fatemeh Pourahmad

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引用次数: 0

摘要

本文研究了一类非光滑非凸一般优化问题的顺序 M-stationarity 条件。我们引入了各种类型的此类条件，并将它们与之前在光滑或凸情况下建立的条件进行了比较。在非光滑稀疏约束优化问题中，我们证明了所得出结果的应用。此外，我们还针对光滑稀疏性问题的特定情况设计了一种拉格朗日型算法。本文列举了几个例子来说明结果。

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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Sequential M-Stationarity Conditions for General Optimization Problems

In this paper, we investigate sequential M-stationarity conditions for a class of nonsmooth nonconvex general optimization problems. We introduce various types of such conditions and compare them with previously established conditions in smooth or convex cases. The application of the derived results is demonstrated in the context of nonsmooth sparsity-constrained optimization problems. Additionally, we devise a Lagrangian-type algorithm for a specific case of smooth sparsity problems. Several examples are presented throughout the paper to illustrate the results.

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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.