中文
Published date:2014-12-15    Provided by:School of Science
Title: Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming and Beyond

Guest Speaker: Dr. Xiaoming Yuan (Hong Kong Baptist University)

Time: 2014-12-17 (Wednesday), 1030 - 1200
Location:
Conference Room 7215, School of Science


Abstract

      The alternating direction method of multipliers (ADMM) is a benchmark for solving a linearly constrained convex minimization model with a two-block separable objective function; and it has been shown that its direct extension to a multiple-block case where the objective function is the sum of more than two functions is not necessarily convergent. For the multiple-block case, a natural idea is to artificially group the objective functions and the corresponding variables as two groups and then apply the original ADMM directly - the block-wise ADMM is accordingly named because each of the resulting ADMM subproblems may involve more than one function in its objective. Such a subproblem of the block-wise ADMM may not be easy as it may require minimizing more than one function with coupled variables simultaneously. We discuss how to further decompose the block-wise ADMMs subproblems and obtain easier subproblems so that the properties of each function in the objective can be individually and thus effectively used, while the convergence can still be ensured. Extensions to the block-wise versions of the generalized ADMM and the ADMM with Gaussian back substitution will also be discussed.

Biography

      Xiaoming Yuan(袁晓明)was educated at Nanjing University (B.Sc., M.Phil.) and City University of Hong Kong (Ph.D.), all majoring in Mathematics. He had worked at University of Victoria, Shanghai Jiao Tong University, and University of British Columbia Okanagan before he joined Hong Kong Baptist University.

       His research focus is numerical optimization including such topics as variational inequalities and complementarity problems, sparse and lowrank optimization, and firstorder methods for largescale convex programming problems. Xiaoming Yuan is also interested in applications arising in image processing, statistics and operations management.

      His research works have appeared in some top journals such as SIAM Journal on Optimization, Mathematics of Computation, Journal of Scientific Computing and Math. Programming.