A Cutting-Surface Theory for Mixed-Integer Conic Programs
In this talk, we discuss our recent developments in the design of algorithmic tools for MICP. Inspired by the pivotal role of disjunctive cutting-planes in the algorithmic advances for MILP, we develop the theory of disjunctive cutting-surfaces for mixed-integer second order cone programming (MISOCP). To this end, we consider two-term disjunctions on the second-order cone and its affine cross-sections. The resulting nonconvex sets are of fundamental importance in MISOCP where they can be used to derive valid inequalities that strengthen the problem formulation. We identify the cases where the convex hull of the disjunction can be completely characterized with a single second-order conic inequality, allowing efficient computation with second-order cone programming in a cutting-surface algorithm framework. This talk is based on joint works with Fatma Kilinc-Karzan and Gerard Cornuejols.
Bio: Sercan Yildiz is a PhD candidate in Algorithms, Combinatorics, and Optimization in the Tepper School of Business of Carnegie Mellon University. Previously, he received a master's degree in Algorithms, Combinatorics, and Optimization from Carnegie Mellon University and master's and bachelor's degrees in Industrial Engineering from the University of Pittsburgh and Bogazici University, respectively. His research centers on operations research, with emphasis on the methodological and practical aspects of integer programming and non-convex optimization.