A Study of Geodesic ( E, F )-Preinvex Functions on Riemannian Manifolds

Ehtesham Akhter, Mohd Bilal and Musavvir Ali ()
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Ehtesham Akhter: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Mohd Bilal: Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Musavvir Ali: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2025, vol. 13, issue 6, 1-9

Abstract: In this manuscript, we define the ( E , F ) -invex set, ( E , F ) -invex functions, and ( E , F ) -preinvex functions on Euclidean space, i.e., simply vector space. We extend these concepts on the Riemannian manifold. We also detail the fundamental properties of ( E , F ) -preinvex functions and provide some examples that illustrate the concepts well. We have established a relation between ( E , F ) -invex and ( E , F ) -preinvex functions on Riemannian manifolds. We introduce the conditions A and define the ( E , F ) -proximal sub-gradient. ( E , F ) -preinvex functions are also used to demonstrate their applicability in optimization problems. 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 the ( E , F ) -proximal sub-gradient.

Keywords: Riemannian manifolds; geodesic (E, F)-invex sets; functions; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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