Ethan X Fang, Bingsheng He, Han Liu, Xiaoming Yuan
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引用次数: 109
Abstract
Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worst-case 𝒪(1/k) convergence rate measured by the iteration complexity (k represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.
期刊介绍：
Mathematical Programming Computation (MPC) publishes original research articles advancing the state of the art of practical computation in Mathematical Optimization and closely related fields. Authors are required to submit software source code and data along with their manuscripts (while open-source software is encouraged, it is not required). Where applicable, the review process will aim for verification of reported computational results. Topics of articles include:
New algorithmic techniques, with substantial computational testing
New applications, with substantial computational testing
Innovative software
Comparative tests of algorithms
Modeling environments
Libraries of problem instances
Software frameworks or libraries.
Among the specific topics covered in MPC are linear programming, convex optimization, nonlinear optimization, stochastic optimization, integer programming, combinatorial optimization, global optimization, network algorithms, and modeling languages.
MPC accepts manuscript submission from its own editorial board members in cases in which the identities of the associate editor, reviewers, and technical editor handling the manuscript can remain fully confidential. To be accepted, manuscripts submitted by editorial board members must meet the same quality standards as all other accepted submissions; there is absolutely no special preference or consideration given to such submissions.
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