In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions … Read more
In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance … Read more
We investigate a network design problem under traffic uncertainty which arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network so as to support all … Read more
We study multi-period nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasi-convexity of the optimal value function of certain subproblems is sufficient for the reducibility of the resulting robust optimization … Read more
For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single and multiple period settings. We show that the problem of finding the “most robust” profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe … Read more
In this paper we present a methodology to decide capacity expansions for a transit network that finds a robust solution with respect to the uncertainty in demands and travel times. We show that solving for a robust solution is a computationally tractable problem under conditions that are reasonable for a transportation system. For example, the … Read more
Linear programming problems with fuzzy coefficients in the objective function are considered. Emphasis is on the dependence of the optimal solution from linear perturbations of the membership functions of the objective function coefficients as well as on the computation of a robust solution of the fuzzy linear problem if the membership functions are not surely … Read more
We describe strong mixed-integer programming formulations for robust mixed 0-1 programming with uncertainty in the objective coefficients. In particular, we focus on an objective uncertainty set described as a polytope with a budget constraint. We show that for a robust 0-1 problem, there is a tight linear programming formulation with size polynomial in the size … Read more
In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone, and study … Read more
Based on the recent approach of Bertsimas and Sim \cite{bs1, bs2} to robust optimization in the presence of data uncertainty, we prove a bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. A … Read more