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An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization

Chengbo Li(cl9***at***rice.edu)
Wotao Yin(wotao.yin***at***rice.edu)
Hong Jiang(hong.jiang***at***alcatel-lucent.com)
Yin Zhang(yzhang***at***rice.edu)

Abstract: Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration. We establish convergence for this algorithm, and apply it to solving problems in image reconstruction with total variation regularization. We present numerical results showing that the resulting solver, called TVAL3, is competitive with, and often outperforms, other state-of-the-art solvers in the field.

Keywords: total variation, compressive sensing, augmented Lagrangian method, nonmonotone line search, Barzilai-Borwein method

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: TR12-13, Computational and Applied Mathematics, Rice University, Houston, TX

Download: [PDF]

Entry Submitted: 08/13/2012
Entry Accepted: 08/13/2012
Entry Last Modified: 08/13/2012

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