Jan Kronqvist: (Convex) mixed-integer optimization: some algorithms and modeling techniques

Abstract

The presentation focuses on how to efficiently solve optimization problems containing some integer variables (variables restricted to integer values). The integer restrictions can originate from disjunctions, logical relations, or general integer properties of some of the variables. Some algorithms for solving so-called convex MINLP problems are described in the presentation, and we briefly analyze some of their properties. A technique for deriving strong cuts (linear inequalities satisfied for all integer feasible solutions but violated for some fractional solutions) based on disjunctive structures of convex MINLP problems is also presented. A new approach for modeling disjunctive terms is briefly presented along with an application in verification of ReLU-based neural networks. The presentation is intended to give a brief overview of several topics in mixed-integer optimization and some of the presenter’s research interests.