Divya Padmanabhan

Distributionally robust optimization through the lens of submodularity

Categories Convex Optimization, Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , ,

In this paper, we propose submodular ambiguity sets for distributionally robust optimization and showcase its usefulness in modeling discrete and continuous uncertainty. From a modeling perspective, we propose two new tractable submodular ambiguity sets that combine marginal distributions and covariance information for discrete uncertainty and mean and covariance information for continuous uncertainty. From a computational … Read more

Tree Bounds for Sums of Bernoulli Random Variables: A Linear Optimization Approach

Categories Combinatorial Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

We study the problem of computing the tightest upper and lower bounds on the probability that the sum of n dependent Bernoulli random variables exceeds an integer k. Under knowledge of all pairs of bivariate distributions denoted by a complete graph, the bounds are NP-hard to compute. When the bivariate distributions are specified on a … Read more

Exploiting Partial Correlations in Distributionally Robust Optimization

Categories Polyhedra, Robust Optimization, Semi-definite Programming Tags , , ,

In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more