Seminar Series | The ADMM: Past, Present, and Future
270 Journalism Building
242 W 18th Ave
Columbus, OH 43210
Speaker: Jonathan Eckstein, Rutgers University
Title: The ADMM: Past, Present, and Future
Abstract: Over the past 15 years, the alternating direction method of multipliers (ADMM) has become a standard optimization method. This talk will cover the origins of the ADMM, its subsequent development, and what to expect in the future.
The origins of the ADMM are somewhat unusual in that it was discovered computationally before it was analyzed. Its convergence analysis is also noteworthy because, while the ADMM may outwardly appear to be a dual ascent method, the natural analyses center on reducing the distance to certain fixed points combining primal and dual variables. The nature of these analyses explains the difficulty of proving convergence of natural variants of the algorithm that change the penalty parameter between iterations or involve sums of more than two functions.
We will also cover some currently known variations on the ADMM and the problem formulation features that tend to distinguish between successful and unsuccessful applications. Finally, the talk will briefly address what we may expect for the future and what other operator splitting methods might become viable members of the optimization toolbox.
Bio: Jonathan Eckstein is a Distinguished 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 (including the ADMM and related splitting methods) and branch-and-bound algorithms. He has also worked on stochastic programming, 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. (a pioneer of highly parallel computing systems) 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). In 2019, he became editor-in-chief of the journal /Mathematical Programming Computation/.