Inexact alternating direction methods of multipliers for separable convex optimization

William W. Hager () and Hongchao Zhang ()
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William W. Hager: University of Florida
Hongchao Zhang: Louisiana State University

Computational Optimization and Applications, 2019, vol. 73, issue 1, No 7, 235 pages

Abstract: Abstract Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.

Keywords: Separable convex optimization; Alternating direction method of multipliers; Multiple blocks; Inexact ADMM; Global convergence; 90C06; 90C25; 65Y20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00072-2

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