We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators,...

We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators,...

This paper describes theNeighbourhood Search, an effectivemethod that we suggest for constructing Pareto sets in multiple objective problems with conegenerated orders. TheNeighbourhood Search is then applied to discounted Markov Decision Processes, resulting in original statements about...

This paper describes theNeighbourhood Search, an effectivemethod that we suggest for constructing Pareto sets in multiple objective problems with conegenerated orders. TheNeighbourhood Search is then applied to discounted Markov Decision Processes, resulting in original statements about...

General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their...

This study is based on the analogy between hedging a risky asset and keeping reserves to meet an unknown demand. The optimal hedging level, which depends on individual preferences, is regarded as a measure of risk. We determine the set of optimal levels and investigate the properties of the...

In this paper we present penalty and barrier methods for solving general convex semidefinite programming problems. More precisely, the constraint set is described by a convex operator that takes its values in the cone of negative semidefinite symmetric matrices. This class of methods is an...

In this paper we present penalty and barrier methods for solving general convex semidefinite programming problems. More precisely, the constraint set is described by a convex operator that takes its values in the cone of negative semidefinite symmetric matrices. This class of methods is an...