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This talk describes a new class of splitting methods for monotone operator problems developed by the author and P. Combettes. It can solve problems involving any finite number of operators and can operate in an asynchronous parallel manner. It has a unique feature for a decomposition algorithm: it does not need to visit every monotone operator at each iteration. The coordination step is based on the synchronous projective splitting technique developed by B. F. Svaiter and the author. One application of the method is an algorithm resembling the multi-block alternating direction method of multipliers (ADMM), but capable of highly asynchronous operation without restrictive assumptions on the problem or proximal parameters. Time permitting, we may also discuss an application to stochastic programming.
Jonathan Eckstein is a Professor in the department of Management Science and Information Systems at Rutgers University. His principle research interests are in numerical optimization algorithms, both continuous and discrete, and especially their implementation on parallel computing platforms. Areas of particular focus include augmented Lagrangian/proximal methods, branch-and-bound algorithms, and stochastic programming. He has also worked on risk-averse optimization modeling and on applying O.R. techniques to managing information systems. He completed his Ph.D. in Operations Research at M.I.T. in 1989, and then taught at Harvard Business School for two years. He then spent four years in the Mathematical Sciences Research Group of Thinking Machines, Inc. before joining Rutgers. At Rutgers, he led an effort establishing a new undergraduate major in Business Analytics and Information Technology ("BAIT"). In 2014, he was elected a fellow of INFORMS (the Institute for Operations Research and Management Science).