TITLE:  A Copositive Approach for Two-Stage Adjustable Robust Optimization with Uncertain Right-Hand Sides

(Joint with Guanglin Xu)

Abstract: 

We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which in turn leads to a class of tractable, semidefinite-based approximations that are at least as strong as the affine policy. We investigate several examples from the literature demonstrating that our tractable approximations significantly improve the affine policy. In particular, our approach solves exactly in polynomial time a class of instances of increasing size for which the affine policy admits an arbitrarily large gap.

Bio:

Sam Burer is George Daly Professor and Graduate Business Analytics Director in the Department of Management Sciences at the University of Iowa. He received his Ph.D. from the Georgia Institute of Technology, and his professional interests include analytics, operations research, management sciences, and optimization. His research has been supported by grants from the National Science Foundation, and he serves on the editorial boards of Management Sciences, Operations Research, SIAM Journal on Optimization, and Mathematics of Operations Research. He has also served as a Member of the Board of Directors of the INFORMS Computing Society and as a Council Member of the Mathematical Optimization Society.