(p,r)-Invex Sets and Functions

AbstractNotions 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)-pre-invex 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