Pointwise and Ergodic Convergence Rates of a Variable Metric Proximal Alternating Direction Method of Multipliers

Max L. N. Gonçalves (), Maicon Marques Alves () and Jefferson G. Melo ()
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Max L. N. Gonçalves: Universidade Federal de Goiás
Maicon Marques Alves: Universidade Federal de Santa Catarina
Jefferson G. Melo: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 9, 448-478

Abstract: Abstract In this paper, we obtain global pointwise and ergodic convergence rates for a variable metric proximal alternating direction method of multipliers for solving linearly constrained convex optimization problems. We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient framework for solving monotone inclusions. Then, the convergence rates for the former method are obtained essentially by showing that it falls within the latter framework. To the best of our knowledge, this is the first time that global pointwise (resp. pointwise and ergodic) convergence rates are obtained for the variable metric proximal alternating direction method of multipliers (resp. variable metric hybrid proximal extragradient framework).

Keywords: Alternating direction method of multipliers; Variable metric; Pointwise and ergodic convergence rates; Hybrid proximal extragradient method; Convex program; 90C25; 90C60; 49M27; 47H05; 47J22; 65K10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1232-6

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