New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...

In this paper we present a survey of generalizations of the celebrated Farkas’s lemma, starting from systems of linear inequalities to a broad variety of non-linear systems. We focus on the generalizations which are targeted towards applications in continuous optimization. We also briefly...

We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its...