joint work with Divya Padmanabhan, Karthik Natarajan
We aim to identify partial covariance structures that allow polynomial-time instances for evaluating the worst-case expected value of mixed integer linear programs with uncertain coefficients. Assuming only the knowledge of mean and covariance entries restricted to block-diagonal patterns, we develop a reduced SDP formulation whose complexity is characterized by a suitable projection of the convex hull of rank 1 matrices formed by extreme points of the feasible region. These projected constraints lend themselves to polynomial-time instances in appointment scheduling and PERT network contexts.
joint work with Taozeng Zhu, Melvyn Sim
Many real-world optimization problems have input parameters estimated from data whose inherent imprecision can lead to fragile solutions that may impede desired objectives and/or render constraints infeasible. We propose a joint estimation and robustness optimization (JERO) framework to mitigate estimation uncertainty in optimization problems by seamlessly incorporating both the parameter estimation procedure and the optimization problem.
joint work with Guanglin Xu
We study decision rule approximations for multi-stage robust linear optimization problems. We examine linear decision rules for the generic problem instances and quadratic decision rules for the case when only the problem right-hand sides are uncertain. The decision rule problems are amenable to exact copositive programming reformulations that yield tight, tractable semidefinite programming solution schemes. We prove that these new approximations are tighter than the state-of-the-art schemes and demonstrate their superiority through numerical experiments.