基于共轭的凸上影线的$\varepsilon $次微分方法

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED Set-Valued and Variational Analysis Pub Date : 2024-03-12 DOI:10.1007/s11228-024-00712-8

Rafael Correa, Abderrahim Hantoute, Marco A. López

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引用次数: 0

摘要

我们为任意凸函数族的上确界的（（varepsilon \）-次微分提供了新的特征。由此得到的公式只涉及数据函数的适当凸组合的近似次微分。介绍了具有类似凹凸性质的凸函数族，并研究了它们与仿射模型的关系。还分析了数据函数的下半连续性的作用。

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Conjugation-Based Approach to the $\varepsilon $ -Subdifferential of Convex Suprema

We provide new characterizations of the $\varepsilon $-subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.

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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.

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