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A robust approach to solving linear optimization problems with uncertain data has been proposed in the early 1970s, and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data, in order to ensure that the solution remains feasible and near optimal when the… (More)

We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are… (More)

In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by firstly… (More)

Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of addressing a general class of multistage stochastic… (More)

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information.… (More)

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a… (More)

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures. Our… (More)

Value-at-Risk (VaR) is one of the most widely accepted risk measures in the financial and insurance industries, yet efficient optimization of VaR remains a very difficult problem. We propose a computationally tractable approximation method for minimizing the VaR of a portfolio based on robust optimization techniques. The method results in the optimization… (More)

In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general… (More)