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An extension of the proximal point algorithm beyond convexity

Authors :
Sorin-Mihai Grad
Felipe Lara
University of Vienna [Vienna]
Optimisation et commande (OC)
Unité de Mathématiques Appliquées (UMA)
École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)
Universidad de Tarapaca
Source :
Journal of Global Optimization, Journal of Global Optimization, Springer Verlag, 2021, ⟨10.1007/s10898-021-01081-4⟩
Publication Year :
2021

Abstract

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.

Details

Language :
English
ISSN :
09255001 and 15732916
Database :
OpenAIRE
Journal :
Journal of Global Optimization, Journal of Global Optimization, Springer Verlag, 2021, ⟨10.1007/s10898-021-01081-4⟩
Accession number :
edsair.doi.dedup.....61a8086a0ec87b2b04c0181b2468f6e9