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
Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities “fail” from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to … Read more
For a particular class of minimax stochastic programming models, we show that the problem can be equivalently reformulated into a standard stochastic programming problem. This permits the direct use of standard decomposition and sampling methods developed for stochastic programming. We also show that this class of minimax stochastic programs subsumes a large family of mean-risk … Read more
An optimal control solution to a fed-batch fermentation process, responding to a competition call, was developed using NEOS Server. Substantial improvement to the nominal performance achieved in the paper demonstrates the ability of the NEOS Server and the APPS algorithm. Citation Proceedings of Inst. of Mechanical Engineers , Part-I (UK). To appear. (Accepted May 2003). … Read more
In this paper we combine both trust-region and linesearch globalization strategies in a globally convergent hybrid algorithm to solve a continuously differentiable nonlinear equality constrained minimization problem. First, the trust-region approach is used to determine a descent direction of the augmented Lagrangian chosen as the merit function, and second, linesearch techniques are used to obtain … 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
This paper considers robust optimization to cope with uncertainty about the stock return process in one period portfolio selection problems involving options. The ro- bust approach relates portfolio choice to uncertainty, making more cautious portfolios when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlyings and show that … Read more
Given a real function on a Euclidean space, we consider its “robust regularization”: the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint … Read more
The purpose of this note is to present a robust counterpart of the Huber estimation problem in the sense of Ben-Tal and Nemirovski when the data elements are subject to ellipsoidal uncertainty. The robust counterparts are polynomially solvable second-order cone programs with the strong duality property. We illustrate the effectiveness of the robust counterpart approach … Read more
Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible … Read more