Abstract. Duality theory has played a key role in convex programming in the absence of data uncertainty. In this paper, we present a duality theory for convex programming problems in the face of data uncertainty via robust optimization. We characterize strong duality between the robust counterpart of an uncertain convex program and the optimistic counterpart of its uncertain Lagrangian dual. We...

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

The traveling salesman problem is one of the most famous combinatorial optimization problems, and has been intensively studied in the last decades. Many extensions to the basic problem have been also proposed, with the aim of making the resulting mathematical models as much realistic as possible. We present a new extension to the basic problem, where travel times are specified as a range of pos...

In real-world applications, costs for products are not deterministic: neither static nor dynamic. They actually tend to be non-stationary and cross-correlated. To overcome this drawback, there have been some efforts by researchers to extend the Wagner–Whitin algorithm to consider stochastic costs. However, they assume that the information of probability density function of random costs exists. ...

background and objectives: a sudden jump in blood demand during natural disasters may have strong negative impact on the performance of blood supply chain. appropriate response to the emergency situations, requires predictive approach to determining the optimal allocation of blood supply chain resources for various disaster scenarios. the present study, thus, presents an optimization model aime...

It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski [2] increases the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced in [9] an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show that their method can be ...

A novel robust optimization methodology is proposed for scheduling under bounded uncertainty in processing times. This approach generates “robust” solutions which are in a sense immune against uncertainty when it is applied to Mixed-Integer Linear Programming (MILP) problems with uncertain coefficients and right-hand-side parameters of the inequality constraints. By introducing a small number o...

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain La...

The problem of production management can often be cast in the form of a linear program with uncertain parameters and risk constraints. Typically, such problems are treated in the framework of multi-stage Stochastic Programming. Recently, a Robust Counterpart (RC) approach has been proposed, in which the decisions are optimized for the worst realizations of problem parameters. However, an applic...

in this paper, a robust model presented is developed for hub covering flow problem in which hubs have capacity. this problem has two objective functions converting to a single-objective problem by using weighting method. firstly, the problem will be formulated in a certain case. then, by considering the demand as a non-random variable, it will be modeled by robust optimization. finally, by usin...