On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems

Ron Shefi () and Marc Teboulle ()
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Ron Shefi: Tel-Aviv University
Marc Teboulle: Tel-Aviv University

EURO Journal on Computational Optimization, 2016, vol. 4, issue 1, No 3, 27-46

Abstract: Abstract We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic sublinear rate of convergence for PALM. When the number of blocks is two, and the smooth coupling function is quadratic we present a fast version of PALM which is proven to share a global sublinear rate efficiency estimate improved by a squared root factor. Some numerical examples illustrate the potential benefits of the proposed schemes.

Keywords: Non-smooth convex minimization; Alternating proximal methods; Coordinate descent; Non-asymptotic rate of convergence; 90C25; 49M27; 65K05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13675-015-0048-5

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