[CCoE Notice] Industrial Engineering Seminar

[Tekin, Eylem]

INDUSTRIAL ENGINEERING SEMINAR

Date: April 25, 2014
Time: 10am-11am
Place: 102 D


The Direct Extension of ADMM for Multi-block Convex Minimization Problems

is Not Necessarily Convergent

Yinyu Ye
Professor of Management Science and Engineering
Director, Industrial Affiliates Program of the MS&E
Stanford University
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 alternatively updated. It is strongly desirable and practically valuable to extend ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time - neither affirmatively proved convergence nor counter example showing its failure of convergence is known in the literature. In this paper we answer this long-standing open question: the direct extension of ADMM is not necessarily convergent. We present examples showing its failure of convergence.
Biography

Yinyu Ye received the B.S. degree in System Engineering from the Huazhong University of Science and Technology, Wuhan, China, and the M.S. and Ph.D. degrees in Management Science & Engineering from Stanford University, Stanford. Currently, he is a full Professor of Management Science and Engineering and Institute of Computational and Mathematical Engineering and the Director of the MS&E Industrial Affiliates Program, Stanford University. His current research interests include Continuous and Discrete Optimization, Mathematical Programming, Algorithm Design and Analysis, Computational Game/Market Equilibrium, Metric Distance Geometry, Graph Realization, Dynamic Resource Allocation, and Stochastic and Robust Decision Making, etc.


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