Sensitivity analysis for linear optimization problem with fuzzy data in the objective function

Linear programming problems with fuzzy coefficients in the objective function are considered. Emphasis is on the dependence of the optimal solution from linear perturbations of the membership functions of the objective function coefficients as well as on the computation of a robust solution of the fuzzy linear problem if the membership functions are not surely … Read more

Strong Formulations of Robust Mixed 0-1 Programming

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

Multivariate Nonnegative Quadratic Mappings

In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone, and study … Read more

On Robust 0-1 Optimization with Uncertain Cost Coefficients

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

Robust Option Modelling

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

Optimal Magnetic Shield Design with Second-Order Cone Programming

In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-order cone program, for which efficient primal-dual interior-point algorithms have been developed … Read more

Robust regularization

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 Robust Shortest Path Problem with Interval Data

Motivated by telecommunication applications, we investigate the shortest path problem on directed acyclic graphs under arc length uncertainties represented as interval numbers. Using a minimax-regret criterion we define and identify robust paths via mixed-integer programming and exploiting interesting structural properties of the problem. Citation Bilkent University, Department of Industrial Engineering, Technical Report August 2001 Article … Read more

On Robust Optimization of Two-Stage Systems

Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to … Read more