Saddle point type optimality criteria for optimization problems over cone

In this paper, concepts of arcwise cone-connected mappings, *-arcwise semi differentiability, *-pseudo cone-connected mappings and *-quasi cone-connected mappings are introduced in infinite dimensional spaces. Fritz John and Karush–Kuhn–Tucker type necessary and sufficient conditions are given for a weak minimum and a minimum of the optimization problem over cones. These conditions are then used to study saddle point optimality criteria in terms of a Lagrangian function.