I am an assistant professor in the Grado Department of Industrial and Systems Engineering (ISE) at Virginia Tech. I obtained my PhD at the University of California, Davis under the supervision of Matthias Köppe. Afterwards, I spent two years in Zurich, Switzerland as a postdoctoral researcher at the Institute for Operations Research in the Department for Mathematics at ETH Zurich. Subsequently, I was a Goldstine Fellow Postdoctoral Researcher at IBM Watson Research Center in Yorktown Heights, New York. I recently participated in the semester long Simons Institute program on Bridging Continuous and Discrete Optimization at UC Berkeley. E-mail: rhil@vt.edu Research interestsI am broadly interested in complexity and geometry of optimization problems and applications in operations research. Favorite topics of mine include linear and non-linear integer programming, geometry of numbers, convex geometry, combinatorics, operations research, machine learning, and sub modular optimization. List of collaborators: Amitabh Basu, Jörg Bader, Stephen R. Chestnut, Sanjeeb Dash, Alberto Del Pia, Oktay Gunluk, Matthias Köppe, Marco Molinaro, Timm Oertel, Robert Weismantel, Kevin Zemmer, Rico Zenklusen, Yuan Zhou This spring, I will be teaching ISE 6416: Integer Programming. More information to come soon. ISMP 2018 - 23rd International Symposium on Mathematical Programming, July 1-6, 2018 Bordeaux (France) (more to come...) Publications Preprints Sublinear Bounds for a Quantitative Doignon-Bell-Scarf Theorem, submitted (with S. R. Chestnut and R. Zenklusen) arxiv.org Journal and refereed conference articles [2017] Minimal cut-generating functions are nearly extreme, extended version, to appear Mathematical Programming (with A. Basu and M. Molinaro) pdf Springer Mixed Integer Reformulations of Integer Programs and the Affine TU-dimension of a Matrix, to appear Mathematical Programming (with J. Bader, R. Weismantel, and R. Zenklusen) arxiv.org Extension Complexity Lower Bounds for Mixed-Integer Extended Formulations, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) (with R. Weismantel and R. Zenklusen) arxiv.org [2016] Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2, Mathematical Programming A (with A. Basu, M. Koeppe) arxiv.org Minimal cut-generating functions are nearly extreme, IPCO 2016 (with A. Basu and M. Molinaro) pdf Springer An FPTAS for Minimizing Indefinite Quadratic Forms Over Integers in Polyhedra, Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016) (with K. Zemmer, R. Weismantel) arxiv.org SIAM [2015] Note on the Complexity of the Mixed-Integer Hull of a Polyhedron, Operations Research Letters (with T. Oertel, R. Weismantel) arxiv.org ScienceDirect Light on the Infinite Group Problem, 4OR (with A. Basu, M. Koeppe) arxiv.org Springer: part 1, part 2 Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane, Mathematics of Operations Research (with A. Del Pia, R. Weismantel, K. Zemmer) arxiv.org MathOR slides [2014] Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem, Mathematics of Operations Research (with A.Basu, M. Koeppe) arxiv.org MathOR [2013] The Triangle Closure is a Polyhedron, Mathematical Programming A (with A. Basu, M. Koeppe) arxiv.org Springer Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem. II. The Unimodular Two Dimensional Case, Proceedings of IPCO 2013 (with A. Basu, M. Koeppe) arxiv.org Springer A (k+1)-Slope Theorem for the k-Dimensional Infinite Group Relaxation, SIAM Journal on Optimization (with A. Basu, M. Koeppe, M. Molinaro) arxiv.org SIAM A new Lenstra-type Algorithm for Quasiconvex Polynomial
Integer Minimization with complexity 2^O(n log n), Discrete Optimization
(with M. Koeppe) arxiv.org, Elsevier ScienceDirect EducationPh.D. in Applied Mathematics, University of California, Davis, June 2013 B.Sc. in Mathematics, University of Puget Sound, May 2008 |