Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-butbounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, (2) tractability of robust counterpa...

This paper proposes a family of robust counterpart for uncertain linear programs (LP) which is obtained for a general definition of the uncertainty region. The relationship between uncertainty sets using norm bod-ies and their corresponding robust counterparts defined by dual norms is presented. Those properties lead us to characterize primal and dual robust counterparts. The researchers show t...

A robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust optimization is used in dealing with impreciseness while an interactive procedure is used in eliciting preference information from the decision maker and in making tradeoffs among the...

The multi-objective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of...

We consider a finite-horizon single-product periodic-review inventory management problem with demand distribution uncertainty. We formulate the problem as a dynamic program and prove the existence of an optimal (s, S) policy. The corresponding dynamic robust counterpart models are then developed for the box and the ellipsoid uncertainty sets. These counterpart models are transformed into tracta...

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 diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to...

A robust optimization framework for countably infinite linear programs (CILPs) is developed. It is shown that a particular robust counterpart of a nominal CILP can be reformulated as another CILP. A bound on the probability of constraint violation is derived. A convergent algorithm for solving this robust CILP is proposed.

Robust optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic uncertain-but-bounded data perturbations. In this paper, we consider the weighted least squares problems where the coefficient matrices and vector belong to different uncertain bounded sets. We introduce the robust counterparts of these problems and reformulate them as the tract...

A considerable amount of optimization problems arising in the control and systems theory field can be seen as special instances of robust optimization. Much of the modeling effort in these cases is spent on converting an uncertain problem to a robust counterpart without uncertainty. Since many of these conversions follow standard procedures, it is amenable to software support. This paper presen...