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A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems

Jiaming Liang (jiaming.liang***at***gatech.edu)
Renato Monteiro (renato.monteiro***at***isye.gatech.edu)

Abstract: This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form f+h where f is a (possibly nonconvex) differentiable function whose gradient is Lipschitz continuous and h is a closed convex function with bounded domain. D-AIPP performs two types of iterations, namely, inner and outer ones. Its outer iterations correspond to the ones of the accelerated inexact proximal point scheme. Its inner iterations are the ones performed by an accelerated composite gradient method for inexactly solving the convex proximal subproblems generated during the outer iterations. Thus, D-AIPP employs both inner and outer accelerations.

Keywords: Nonconvex Optimization, Iteration-Complexity, First-Order Accelerated Method, Proximal Point Method

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization


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Entry Submitted: 11/26/2018
Entry Accepted: 11/27/2018
Entry Last Modified: 12/17/2018

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