Strict (ε, δ)-Subdifferentials and Extremality Conditions

Abstract

A new abstract definition of extremality is introduced extending traditional extremality notions in optimization problems. The set of points satisfying the new definition includes points not necessarily optimal in the usual sense but nevertheless having some extremal properties. Necessary and sufficient extremality conditions are derived. Contrary to usual notions of extremality the new one is stable relative to small deformations of the data.

Keywords:

• Nonsmooth Analysis
• Subdifferentials
• Normal Cones
• Optimality Conditions
• Set-valued Mappings
• Asplund Spaces