Abstract
AbstractWe 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.
Funder
Austrian Science Fund
Deutsche Forschungsgemeinschaft
Fondo de Fomento al Desarrollo Científico y Tecnológico
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Management Science and Operations Research,Control and Optimization,Computer Science Applications
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