부산대학교 도서관

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.
Author(s): Sorin-Mihai Grad [sup.1], Felipe Lara [sup.2] Author Affiliations: (1) grid.10420.37, 0000 0001 2286 1424, Faculty of Mathematics, University of Vienna, , Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria (2) grid.412182.c, 0000 [...]