We propose ARock, an asynchronous parallel algorithmic framework for finding a fixed point to a nonexpansive operator. In the framework, a set of agents (machines, processors, or cores) updates a sequence of randomly selected coordinates of the unknown variable in a parallel asynchronous fashion. As special cases of ARock, novel algorithms in linear algebra, convex optimization, machine learning, distributed and decentralized optimization are introduced. We show that if the nonexpansive operator has a fixed point, then with probability one the sequence of points generated by ARock converges to a fixed point. Very encouraging numerical performance of ARock is observed on solving linear equations, sparse logistic regression, and other large-scale problems in recent data sciences..

**BIOGRAPHY**

Ming Yan is an assistant professor in the Department of Computational Mathematics, Science and Engineering (CMSE) and the Department of Mathematics at Michigan State University. His research interests lie in computational optimization and its applications in image processing, machine learning, and other data-science problems. He received his B.S. and M.S in mathematics from University of Science and Technology of China in 2005 and 2008, respectively, and then Ph.D. in mathematics from University of California, Los Angeles in 2012. After completing his PhD, Ming Yan was a Postdoctoral Fellow in the Department of Computational and Applied Mathematics at Rice University from July 2012 to June 2013, and then moved to University of California, Los Angeles as a Postdoctoral Scholar and an Assistant Adjunct Professor from July 2013 to June 2015..