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Article Dans Une Revue Journal of Global Optimization Année : 2021

An extension of the proximal point algorithm beyond convexity

Résumé

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.

Dates et versions

hal-03429959 , version 1 (16-11-2021)

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Sorin-Mihai Grad, Felipe Lara. An extension of the proximal point algorithm beyond convexity. Journal of Global Optimization, 2021, ⟨10.1007/s10898-021-01081-4⟩. ⟨hal-03429959⟩
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