An extension of the proximal point algorithm beyond convexity

Sorin-Mihai Grad () and Felipe Lara ()
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Sorin-Mihai Grad: University of Vienna
Felipe Lara: Universidad de Tarapacá

Journal of Global Optimization, 2022, vol. 82, issue 2, No 5, 313-329

Abstract: 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.

Keywords: Nonsmooth optimization; Nonconvex optimization; Proximity operator; Proximal point algorithm; Generalized convex function (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-021-01081-4

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