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

Ying Cui (), Xudong Li (), Defeng Sun () and Kim-Chuan Toh ()
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Ying Cui: National University of Singapore
Xudong Li: National University of Singapore
Defeng Sun: National University of Singapore
Kim-Chuan Toh: National University of Singapore

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 15, 1013-1041

Abstract: Abstract 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.

Keywords: Coupled objective function; Convex quadratic programming; Majorization; Iteration complexity; Nonsmooth analysis; 90C25; 68Q25; 65K05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-016-0877-2

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