On Properties of Geodesic Semilocal E-Preinvex Functions

TL;DR

This paper introduces a new class of functions called geodesic semilocal E-preinvex functions on Riemannian manifolds, explores their properties, and applies them to nonlinear fractional multiobjective programming, establishing optimality and duality results.

Contribution

It defines and analyzes geodesic semilocal E-preinvex functions, extending existing convexity concepts, and applies these to derive optimality conditions and duality theorems in fractional programming.

Findings

Properties of geodesic semilocal E-preinvex functions are established.

Optimality conditions for fractional multiobjective programming are derived.

Duality results are proved using generalized convexity concepts.

Abstract

The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E-$ \eta $-semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-prinvex functions and geodesic quasi-semilocal E-preinvex functions.