# Robert Hildebrand

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 interests

I 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

### Education

Ph.D. in Applied Mathematics, University of California, Davis, June 2013

B.Sc. in Mathematics, University of Puget Sound, May 2008

# Mixed Integer Linear Programming

MILP is an extremely powerful tool that is used in many important applications. The study of includes much beautiful theory using convex analysis, polyhedral theory, submodularity, combinatorics, and much more.

# Branching on Binary Variables

Branching on binary variables with most binarizations can create very little progress in reducing the combined linear relaxations. If you do branch on binary variables, the order of branching is extremely important. Essentailly no progress is realized until variables with the largest coefficients are branched on.

# Comparing Binarizations

Given two binarizations $B_1$ and $B_2$, we can show that $B_2$ is stronger than $B_1$ whenever there is an integral affine transformation $f$ from $B_1$ to $B_2$.