arXiv subjects

Ehtesham Akhter

Publications and source records attributed to Ehtesham Akhter.

5 recordsLinked to original sources

arXiv2023

A study of Geodesic (E, F)-preinvex Functions on Riemannian Manifolds

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.

math.OC↗

arXiv2023

On Some Characterizations of General s-Convex Functions

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain fundamental characteristics of general s-convex functions are discussed for both general cases and differentiable situations. Aside from that, the general s-convexity is used to define and demonstrate the sufficient criteria for optimality for both unconstrained and inequality-constrained programming.

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arXiv2023

On Some Characterization of GS-exponential kind of Convex Functions

This manuscript introduces the idea of GS-exponential kind of convex functions and some of their algebraic features, and we introduce a new class GS-exponential kind of convex sets. In addition, we describe certain fundamental GS-exponential kind of convex function with characteristics in both the general and the differentiable cases. We establish the sufficient conditions of optimality and offer the proof for unconstrained as well as inequality-constrained programming while considering the assumption of GS-exponential kind of convexity.

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arXiv2022

w-Invexity and Optimality Problem

We define w-invex set, w-preinvex, w-strictly preinvex, w-quasi preinvex, w-strictly quasi preinvex, w-semi-strictly quasi preinvex, and w-pre pseudo-invex functions in this context. And these form a class of real functions, which is the generalization of a family of preinvex functions. Here, we provide a thorough analysis of the core characteristics of these functions, along with numerous examples that help to illustrate the idea. Finally, w-quasi preinvex, w-strictly preinvex, and w-strictly quasi preinvex functions are used to analyze the optimization problems.

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arXiv2022

$X$-convexity and Applications of Quasi-$X$-Convex Functions

A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly quasi-$X$-convex functions. Moreover, in this paper, we give a detailed study of the fundamental properties of these functions with various examples, supporting the concepts. Finally, the study of optimization problems employs quasi-$X$-convex, semistrictly quasi-$X$-convex, and strictly quasi-$X$-convex functions.

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