Fixing and extending some recent results on the ADMM algorithm

Sebastian Banert, Radu Ioan Boţ, Ernö Robert Csetnek

Type: Article

Publication Date: 2020-05-14

Citations: 13

DOI: https://doi.org/10.1007/s11075-020-00934-5

Abstract

We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269-297, 2014) in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration, we allow the use of variable metrics, while the investigations are carried out in the setting of infinite-dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.

Locations

Numerical Algorithms - View - PDF
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+ PDF Chat	Variable metric quasi-Fejér monotonicity	2012	Patrick L. Combettes Bằng Công Vũ
+	Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization	2014	Ron Shefi Marc Teboulle
+	Hankel Matrix Rank Minimization with Applications to System Identification and Realization	2013	Maryam Fazel Ting Kei Pong Defeng Sun Paul Tseng
+ PDF Chat	On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators	1992	Jonathan Eckstein Dimitri P. Bertsekas
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+	Some Saddle-function splitting methods for convex programming	1994	Jonathan Eckstein