<Para ID="Par1">Data for optimization problems often comes from (deterministic) forecasts, but it is naïve to consider a forecast as the only future possibility. A more sophisticated approach uses data to generate alternative future scenarios, each with an attached probability. The basic idea is to estimate...</para>

We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our...

We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our...

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex...

In this paper we prove a general version of the Second Welfare Theorem for a non-convex and non-transitive economy, with public goods and other externalities in consumption. For this purpose we use the sub-gradient to the distance function (normal cone) to define the pricing rule in this general...

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex...