Multivariate marginal bounds for probabilistic optimization problems Seminar

Given an optimization problem with an arbitrary cover of random objective coefficients, we evaluate the tightest possible bound on the expected optimal value over all joint distributions consistent with the given multivariate marginals of the elements in the cover. We discuss the computational tractability of the evaluation of the tight bound and the construction of the extremal distributions that achieve the bound, especially when the marginals are non-overlapping. We apply the proposed model for PERT networks to evaluate the bounds for project tardiness and show that the minimax two-stage project crashing problem under the discrete multivariate marginal assumption is tractable. This is joint work with Karthik Natarajan and Xiaobo Li.