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 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.jl. Finally, we introduce the Julia-based interior

point solver for general non-symmetric cones Hypatia.jl, and show how

its use of non-standard cones can allow it to outperform commercial

solvers in certain instances.

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 energy,

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 and the

INFORMS Computing Society Prize. He is currently an associate editor

for Operations Research and Operations Research Letters, a member of

the board of directors of the INFORMS Computing Society, and a member

of the NumFocus steering committee for JuMP.