Keivan Shariatmadar

Constrained optimization problems under uncertainty with coherent lower previsions

We investigate a constrained optimization problem with uncertainty about constraint parameters. Our aim is to reformulate it as a (constrained) optimization problem without uncertainty. This is done by recasting the original problem as a decision problem under uncertainty. We give results for a number of different types of uncertainty models-linear and vacuous previsions, and possibility distributions-and for two common but different optimality criteria for such decision problems-maximinity and maximality. We compare our approach with other approaches that have appeared in the literature.

Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possibility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncertainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.

Implementation of maximin and maximal solutions for linear programming problems under uncertainty

We present a software implementation of the methods for solving linear programming problems under uncertainty from previous work. Uncertainties about constraint parameters can be expressed as intervals or trapezoidal possibility distributions. The software computes the solutions for the optimality criteria maximin and maximality. For maximality with possibility distributions, only an approximate solution is obtained.