Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity with applications to variational inequality, conic constrained saddle point, and convex conic optimization problems
Abstract:In this paper we consider a class of structured monotone inclusion (MI) problems that consist of finding a zero in the sum of two monotone operators, in which one is maximal monotone while another is locally Lipschitz continuous. In particular, we first propose a primal-dual extrapolation (PDE) method for solving a structured strongly MI problem by modifying the classical forward-backward splitting method by using a point and operator extrapolation technique, in which the parameters are adaptively updated by a… Show more
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