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• W2113171505 abstract "The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternately updated. It is computationally beneficial to extend the ADMM directly to the case of a multi-block convex minimization problem. Unfortunately, such an extension fails to converge even when solving a simple square system of linear equations. In this paper, however, we prove that, if in each step one randomly and independently permutes the updating order of any given number of blocks followed by the regular multiplier update, the method will converge in expectation for solving the square system of linear equations. Our result indicates that for ADMM the cyclic update rule and the random permutation update rule are fundamentally different. To the best of our knowledge, this is the first example that such a difference is rigorously established for a specific optimization algorithm, although the random permutation rule has been reported to be experimentally better than the cyclic rule in many large-scale optimization problems. Our analysis technique of random permutation might be useful in other contexts." @default.
• W2113171505 created "2016-06-24" @default.
• W2113171505 creator A5028963874 @default.
• W2113171505 creator A5041526408 @default.
• W2113171505 creator A5091724499 @default.
• W2113171505 date "2015-03-22" @default.
• W2113171505 modified "2023-09-27" @default.
• W2113171505 title "On the Expected Convergence of Randomly Permuted ADMM" @default.
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• W2113171505 hasPublicationYear "2015" @default.
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