Necessary optimality conditions with a modified subdifferential

Abstract

The concepts of the τ-subgradient and τ-subdifferential are introduced for local Lipschitz functions. It is proved that the generalized invex functions have a nonempty τ-subdifferential. The generalized directional derivate related to the τ-subdifferential is given. The necessary conditions of inequality constrained problems are clarified by the τ-subdifferential.

AMS 1980 Subject Classification:

• Primary: 90 C 30

Keywords:

• τ-subgradient
• τ-subdifferential
• generalized invex condition
• τ-generalized directional derivate
• τ-extended directional derivate
• nonconvex nonsmooth necessary optimality condition