p r -Invex Sets and Functions

Notions of invexity of a function and of a set are generalized.The notion of an invex function with respect to η can be further extended with the aid of p-invex sets.Slight generalization of the notion of p-invex sets with respect to η leads to a new class of functions.A family of real functions called, in general, p r -preinvex functions with respect to η (without differentiability) or p r -invex functions with respect to η (in the differentiable case) is introduced.Some (geometric) properties of these classes of functions are derived.Sufficient optimality conditions are obtained for a nonlinear programming problem involving p r -invex functions with respect to η.