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. (arXiv:2206.00973v2 [math.OC] UPDATED)

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 backtracking …

applications arxiv inequality math optimization