solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3291次
Abstract convex approximations of nonsmooth functions. (arXiv:1810.00979v1 [math.OC])
来源于:arXiv
In this article we utilise abstract convexity theory in order to unify and
generalize many different concepts from nonsmooth analysis. We introduce the
concepts of abstract codifferentiability, abstract quasidifferentiability and
abstract convex (concave) approximations of a nonsmooth function mapping a
topological vector space to an order complete topological vector lattice. We
study basic properties of these notions, construct elaborate calculus of
abstract codifferentiable functions and discuss continuity of abstract
codifferential. We demonstrate that many classical concepts of nonsmooth
analysis, such as subdifferentiability and quasidifferentiability, are
particular cases of the concepts of abstract codifferentiability and abstract
quasidifferentiability. We also show that abstract convex and abstract concave
approximations are a very convenient tool for the study of nonsmooth extremum
problems. We use these approximations in order to obtain various necessary
optimality condition 查看全文>>