On the Convergence Properties of a Majorized Alternating Direction Method of Multipliers for Linearly Constrained Convex Optimization Problems with Coupled Objective Functions

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• 作者：Ying Cui ; Xudong Li ; Defeng Sun…
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：169
• 期：3
• 页码：1013-1041
• 全文大小：591 KB
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：169

文摘

In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers for linearly constrained convex optimization problems, whose objectives contain coupled functions. Our convergence analysis relies on the generalized Mean-Value Theorem, which plays an important role to properly control the cross terms due to the presence of coupled objective functions. Our results, in particular, show that directly applying two-block alternating direction method of multipliers with a large step length of the golden ratio to the linearly constrained convex optimization problem with a quadratically coupled objective function is convergent under mild conditions. We also provide several iteration complexity results for the algorithm.KeywordsCoupled objective functionConvex quadratic programmingMajorizationIteration complexityNonsmooth analysis