A study of Geodesic (E, F)-preinvex Functions on Riemannian Manifolds
Abstract
In this manuscript, we define (E, F)-invex set, (E, F)-invex functions, and (E, F)-preinvex functions on Euclidean space. We explore the concepts on the Riemannian manifold. We also detail the fundamental properties of (E, F)-preinvex functions and some examples that illustrate the concepts well. We have established a relation between (E, F)-invex and (E, F)-preinvex functions on the Riemannian manifolds. We introduce the conditions A and define (E, F)-proximal sub-gradient. To explore and demonstrate its applicability to optimization problems, (E, F)-preinvex is utilized. In the last, we establish the points of extrema of a non-smooth (E, F)-preinvex functions on (E, F)-invex subset of the Riemannian manifolds by using (E, F)-proximal sub-gradient.
Keywords
Cite
@article{arxiv.2311.09723,
title = {A study of Geodesic (E, F)-preinvex Functions on Riemannian Manifolds},
author = {Ehtesham Akhter and Musavvir Ali},
journal= {arXiv preprint arXiv:2311.09723},
year = {2023}
}