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Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

Max Gonçalves(maxlng***at***ufg.br )
Jefferson Melo(jefferson***at***ufg.br)
Renato Monteiro(monteiro***at***isye.gatech.edu)

Abstract: This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval (0,2). To the best of our knowledge, all related papers in the literature only consider the case where the over-relaxation parameter lies in the interval (0, (1 + \sqrt{5})/2).

Keywords: alternating direction method of multipliers (ADMM), nonconvex program, pointwise iteration-complexity, first-order methods.

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Convex and Nonsmooth Optimization

Citation:

Download: [PDF]

Entry Submitted: 02/03/2017
Entry Accepted: 02/03/2017
Entry Last Modified: 02/03/2017

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