Multiobjective Programming under Generalized Type I Invexity

AbstractIn this paper we extend a (scalarized) generalized type-I invexity into a vector invexity (V-type I). A number of sufficiency results are established using Lagrange multiplier conditions and under various types of generalized V-type I requirements. Weak, strong, and converse duality theorems are proved in the generalized V-invexity type I setting

Roughly geodesic B - r-preinvex functions on Cartan Hadamard manifolds

In this article, we introduce a new class of functions called roughly geodesic B????r????preinvex on a Hadamard manifold and establish some properties of roughly geodesic B - r-preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on Hadamard manifolds. The results presented in this paper extend and generalize the results appeared in the literature