Steepest Geometric Descent for Regularized Quasiconvex Functions

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-08-23 DOI:10.1007/s11228-024-00731-5

Aris Daniilidis, David Salas

引用次数: 0

Abstract

We establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process flow induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in a more general setting.

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正则化准凸函数的最陡几何下降法

我们建立了从正则局部 Lipschitz 准凸函数的几乎每一点出发的最陡下降曲线的存在性，其中正则性意味着由子级集引起的扫频过程流是可逆的。然后，我们利用最大卷积来正则化一般的类凸函数，并在更一般的情况下获得了性质相同的结果。

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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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.