On properties of geodesic semilocal E-preinvex functions

The authors define a class of functions on Riemannian manifolds, which are calledgeodesic semilocal E-preinvex functions, as a generalization of geodesic semilocalE-convex and geodesic semi E-preinvex functions, and some of its properties areestablished. Furthermore, a nonlinear fractional multiobjective programming isconsidered, where the functions involved are geodesic E-η-semidifferentiability,sufficient optimality conditions are obtained. A dual is formulated and duality resultsare proved by using concepts of geodesic semilocal E-preinvex functions, geodesicpseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvexfunctions.

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