Tuesday, November 28, 2017 at 4:15pm
Linear mixed integer programming (MIP) is an indispensable tool in Operations Research. However, it is often useful to additionally incorporate discrete variables into nonlinear models to better represent intricate optimization problems. This leads to nonlinear MIP and in particular to mixed integer convex optimization (MICONV), which results from adding discrete variables to a convex optimization problem. While more restrictive than general nonlinear MIP, MICONV already has a wide range of applications and they can be significantly easier to solve than general nonlinear MIP.
Similar to linear MIP, there are many MICONV formulation techniques and their characteristics can have a strong effect on solve times. Unfortunately, our understanding of MICONV formulations is significantly more limited than that of linear MIP formulations. In this talk we explore two topics on MICONV formulations. The first topic concerns what can be modeled or represented with MICONV and is joint work with Miles Lubin and Ilias Zadik. Here we give necessary and sufficient conditions for MICONV representability under various restrictions. The second part concerns the construction of small and strong MICONV formulations for unions of convex sets. Here we describe a geometric construction technique and consider the algebraic representability of the resultant formulations.
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 Letters.