A Novel Direction in Mixed Integer Polynomial Optimization: Structural Properties, Polyhedral Approximations, and Global Optimization Algorithms

2017 - presentpresent

This project introduces a novel approach for convexifying a class of notoriously difficult nonconvex sets, that has been the subject of extensive research over the last three decades by the mathematical programming community. By building upon and combining ideas from discrete and continuous optimization along with a novel hypergraph-based representation technique, our research will provide sharp and cheaply computable convex relaxations of several hard nonconvex optimization problems. In addition, this approach will unify and extend several existing theoretical results from combinatorial optimization and global optimization communities. Successful resolution of the research goals of this project will potentially transform solver technology for MINLP problems containing multilinear or polynomial subexpressions, a very powerful framework that subsumes many real-world optimization problems.