(Ф₁,Ф₂)convexity

Abstract

Convexity of a function and of a set are generalized. The new class being introduced, include many well known classes as its subclasses. The defining functions involved are required to satisfy certain regularity conditions. Some properties are studied with or without differentiability; in the differentiable case, first and second order conditions are stated

Keywords:

• Generalized convexity
• first order conditions
• second order conditions
• nonlinear programming