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Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs

Weiwei Kong (wkong37***at***gatech.edu)
Jefferson Melo (jefferson***at***ufg.br)
Renato Monteiro (monteiro***at***isye.gatech.edu)

Abstract: This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form f + h where f is a differentiable function whose gradient is Lipschitz continuous and h is a closed convex function with a bounded domain. The method, basically, consists of applying an accelerated inexact proximal point method for solving approximately a sequence of quadratic penalized subproblems associated to the linearly constrained problem. Each subproblem of the proximal point method is in turn approximately solved by an accelerated composite gradient method. We show that in at most O(1/p^3) the proposed scheme generates a p-approximate stationary point for the linearly constrained problem.

Keywords: quadratic penalty method, nonconvex program, iteration-complexity, proximal point method, first-order accelerated methods.

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

Citation:

Download: [PDF]

Entry Submitted: 01/22/2018
Entry Accepted: 01/22/2018
Entry Last Modified: 02/10/2018

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