This talk focuses on a class of algorithms, called coordinate update algorithms, which are useful at solving large-sized problems involving linear and nonlinear mappings, and smooth and nonsmooth functions. They decompose a problem to simple subproblems, where each subproblem updates one, or a small block of, variables each time. They have found applications throughout signal/imaging processing, differential equations, and machine learning. We abstract many problems to the fixedpoint problem x^{k+1}=Tx^k. This talk discusses the favorable structures of the operator T that enable highly efficient coordinate update iterations. It can be carried out in sequential, parallel, or async-parallel fashions. We introduce new scalable coordinate-update algorithms to many problems involving coupling constraints Ax=b, composite nonsmooth functions f(Ax), and large-scale data. We will present a software package and its numerical examples. This is joint work with Brent Edmunds, Zhimin Peng and Tianyu Wu (UCLA), Yangyang Xu (IMA), and Ming Yan (MSU).
Wotao Yin is a professor in the Department of Mathematics of UCLA. He works ob computational optimization and its applications in image processing, machine learning, and other inverse problems. He received his B.S. in mathematics from Nanjing University in 2001, and then M.S. and Ph.D. in operations research from Columbia University in 2003 and 2006, respectively. During 2006 - 2013, he was with Rice University. He won NSF CAREER award in 2008, Alfred P. Sloan Research Fellowship in 2009, and Morningside Medal in 2016. |

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