In the conic formulation of a convex optimization problem the constraints are expressed as linear inequalities with respect to a possibly non-polyhedral convex cone. This makes it possible to formulate elegant extensions of interior-point methods for linear programming to general nonlinear convex optimization. Recent research on cone programming algorithms has particularly focused on three conv...

We show that in reflexive Banach spaces there are two classes of closed cones (consumption sets) i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. We prove that in the first category of these cones the demand correspondence of any upper semicontinuous preference relation exists and we show also that this property characterizes the reflexive spaces. Moreover...