An extension of the proximal point algorithm beyond convexity

被引：0
作者：
Sorin-Mihai Grad
Felipe Lara
机构：
[1] University of Vienna,Faculty of Mathematics
[2] Universidad de Tarapacá,Departamento de Matemática, Facultad de Ciencias
来源：
Journal of Global Optimization | 2022年 / 82卷
关键词：
Nonsmooth optimization; Nonconvex optimization; Proximity operator; Proximal point algorithm; Generalized convex function;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however none of these classes fully contains the one of prox-convex functions or is included into it. We show that the classical proximal point algorithm remains convergent when the convexity of the proper lower semicontinuous function to be minimized is relaxed to prox-convexity.
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页码：313 / 329
页数：16
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