Abstract:This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is related to the singleton property, Lipschitz continuity, and monotonicity of the associated proximal operator, and we verify it in various classes of functions, including weakly convex functions, indicator functions of proximally smooth sets, and two specific sphere-related no… Show more
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