In this article, we define a new class of functions on Riemannian manifolds, called geodesic ε-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local ε-invex set.
展开▼
