An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

The proximal point algorithm (PPA) is classical and popular in the community of Optimization. In practice, inexact PPAs which solves the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact PPA with a new inexact criterion for solving convex minimization, and show that the iteration-complexity of this inexact PPA is O(1/k). Then, we show that this inexact PPA is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact PPA with the convergence rate O(1/k) is proposed.