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A Study of Geodesic (E, F)-Preinvex Functions on Riemannian Manifolds
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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.
Title: A Study of Geodesic (E, F)-Preinvex Functions on Riemannian Manifolds
Description:
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.
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