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An Accelerated Linearized Alternating Direction Method of Multipliers

Yuyuan Ouyang(ouyang***at***ufl.edu)
Yunmei Chen(yun***at***math.ufl.edu)
Guanghui Lan(glan***at***ise.ufl.edu)
Eduardo Pasiliao Jr.(pasiliao***at***eglin.af.mil)

Abstract: We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in terms of their dependence on the Lipschitz constant of the smooth component. Moreover, AADMM is capable to deal with the situation when the feasible region is unbounded, as long as the corresponding saddle point problem has a solution. A backtracking algorithm is also proposed for practical performance.

Keywords: convex optimization, alternating direction method of multipliers, augmented Lagrangian method, Lagrange multiplier, complexity

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 02/12/2014
Entry Accepted: 02/12/2014
Entry Last Modified: 02/12/2014

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