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An accelerated inexact proximal point method for solving nonconvex-concave min-max problems

Weiwei Kong (wkong37***at***gatech.edu)
Renato D.C. Monteiro (monteiro***at***isye.gatech.edu)

Abstract: Abstract This paper presents a quadratic-penalty type method for solving linearly-constrained composite nonconvex-concave min-max problems. The method consists of solving a sequence of penalty subproblems which, due to the min-max structure of the problem, are potentially nonsmooth but can be approximated by smooth composite nonconvex minimization problems. Each of these penalty subproblems is then solved by applying an accelerated inexact proximal point method to its corresponding smooth composite nonconvex approximation. Iteration complexity bounds for obtaining approximate stationary points of the linearly-constrained composite nonconvex-concave min-max problem are also established.

Keywords: quadratic penalty method, nonconvex program, iteration-complexity, proximal point method, first-order accelerated methods, nonconvex-concave min-max optimization

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Nonlinear Optimization (Other )


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Entry Submitted: 05/31/2019
Entry Accepted: 05/31/2019
Entry Last Modified: 01/16/2020

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