Jean-Paul Watson, Sandia National Laboratories

Abstract

Although Progressive Hedging (PH) is not guaranteed to converge in the case of non-convex and in particular mixed-integer problems, it has been effectively used as a heuristic in a remarkably wide range of applications. In this talk, we will consider the use of PH for solving stochastic mixed-integer and stochastic non-linear optimization problems, in domains ranging from power systems operations to natural resources management. We focus on key issues that occur in practice regarding non-convergence behaviors and how they are often mitigated in practice. Recent work related to computing lower bounds via PH will be introduced. We then discuss open source implementations of PH, available in the Pyomo (https://na01.safelinks.protection.outlook.com/?url=www.pyomo.org&data=02%7C01%7C%7C7e215235c2e44412fe0708d5b9a25fe2%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636619030308205535&sdata=JU3f86ks3h%2FekR1%2BkqhSZog9zm7K%2Bu%2FthN9Lwi7gcWw%3D&reserved=0) optimization library, and parallel deployment in cluster computing environments. We conclude by highlighting key recent application successes, including power systems operations and planning.

This talk represents joint work with Roger Wets, David Woodruff, Carl Laird, Francisco Munoz, among others.