In this paper we study distributionally robust constraints on risk measures (such<br/>as standard deviation less the mean, Conditional Value-at-Risk, Entropic Value-at-Risk) of decision-dependent random variables. The uncertainty sets for the discrete probability distributions are defined using...

In this paper we propose a methodology for constructing decision rules for in-<br/>teger and continuous decision variables in multiperiod robust linear optimization<br/>problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show...

Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex...

This paper adresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a...

Abstract This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental...

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously...

Abstract: Robust optimization (RO) is a young and active research field that has been mainly developed in the last 15 years. RO techniques are very useful for practice and not difficult to understand for practitioners. It is therefore remarkable that real-life applications of RO are still...

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters...