Further Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization

Caihua Chen (), Min Li () and Xiaoming Yuan ()
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Caihua Chen: Nanjing University
Min Li: Southeast University
Xiaoming Yuan: Hong Kong Baptist University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 3, No 11, 906-929

Abstract: Abstract In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.

Keywords: Convex programming; Alternating direction method of multipliers; Logarithmic-quadratic proximal; Convergence rate; Iteration complexity; 90C25; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0682-8

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