(Φ, ρ)-Invexity in Nonsmooth Optimization

Abstract

In this article, a new class of nonconvex nondifferentiable functions, called locally Lipschitz (Φ, ρ)-invex functions, being introduced, includes many well known classes of nondifferentiable generalized convex functions as its subclasses. Some properties of the introduced class of locally Lipschitz (Φ, ρ)-invex functions are studied. Further, nonsmooth mathematical programming problems involving locally Lipschitz (Φ, ρ)-invex functions are considered. Optimality and Mond–Weir duality results for such a class of nonsmooth optimization problems are established.