Title: Modeling power of mixed integer convex optimization problems and their effective solution with Julia and JuMP

Abstract:
More than 50 years of development have made mixed integer linear programming (MILP) an extremely successful tool. MILP's modeling flexibility allows it describe a wide range of business, engineering and scientific problems, and, while MILP is NP-hard, many of these problems are routinely solved in practice thanks to state-of-the- art solvers that nearly double their machine-independent speeds every year. Inspired by this success, the last decade has seen a surge of activity on the solution and application of mixed integer convex programming (MICP), which extends MILP's versatility by allowing the use of convex constraints in addition to linear inequalities. In this talk we cover various recent developments concerning theory, algorithms and computation for MICP. Solvers for MICP can be significantly more effective than those for more general non-convex optimization, so one of the questions we cover in this talk is what classes of non-convex constraints can be modeled through MICP. We also cover the solution of MICP problems through polyhedral approximation algorithms that exploit the power of extended formulations. Finally, we cover various topics concerning the modeling and computational solution of MICP problems using the Julia programming language and the JuMP modeling language for optimization. In Particular, we show how mixed integer optimal control problems where the variables are polynomials can be easily modeled and solved by seamlessly combining several Julia packages and JuMP extensions with the Julia-written MICP solver Pajarito.

Bio:
Juan Pablo Vielma is the Richard S. Leghorn (1939) Career Development Associate Professor at MIT Sloan School of Management and is affiliated to MIT’s Operations Research Center. Dr. Vielma has a B.S. in Mathematical Engineering from University of Chile and a Ph.D. in Industrial Engineering from the Georgia Institute of Technology. His current research interests include the theory and practice of mixed-integer mathematical optimization and applications in natural resource management, marketing and statistics. In January of 2017 he was named by President Obama as one of the recipients of the Presidential Early Career Award for Scientists and Engineers (PECASE). Some of his other recognitions include the NSF CAREER Award, the INFORMS Computing Society Prize and a first prize in the INFORMS Junior Faculty Interest Group Paper Competition. He served as vice-chair of Integer and Discrete Optimization for the INFORMS Optimization Society and as chair of the INFORMS Section on Energy, Natural Resources, and the Environment. He is currently an associate editor for Operations Research and Operations Research Letters, a member of the NumFocus steering committee for JuMP, and the Faculty Director for the MIT-Chile program of MIT's International Science and Technology Initiatives (MISTI).