arXiv subjects

Hilal Ahmad Bhat

Publications and source records attributed to Hilal Ahmad Bhat.

4 recordsLinked to original sources

arXiv2025

Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation

This article explores fundamental properties of convex interval-valued functions defined on Riemannian manifolds. The study employs generalized Hukuhara directional differentiability to derive KKT-type optimality conditions for an interval-valued optimization problem on Riemannian manifolds. Based on type of functions involved in optimization problems, we consider the following cases: 1. objective function as well as constraints are real-valued; 2. objective function is interval-valued, and constraints are real-valued; 3. objective function as well as constraints are interval-valued. The whole theory is justified with the help of examples. The order relation that we use throughout the paper is a total order relation defined on the collection of all closed and bounded intervals in $\mathbb{R}$.

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arXiv2025

Generalized Hukuhara directional differentiability of interval-valued functions on Riemannian manifolds

In this paper, we show that generalized Hukuhara directional differentiability of an interval-valued function (IVF) defined on Riemannian manifolds is not equivalent to the directional differentiability of its center and half-width functions and hence not to its end point functions. This contrasts with S.-L. Chen's \cite{chen} assertion which says the equivalence holds in terms of endpoint functions of an IVF which is defined on a Hadamard manifold. Additionally, the paper addresses some other inaccuracies which arise when assuming the convexity of a function at a single point in its domain. In light of these arguments, the paper presents some basic results that relate to both the convexity and directional differentiability of an IVF.

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arXiv2024

The Karush-Kuhn-Tucker Optimality Conditions for Multi-Objective Interval-Valued Optimization Problem on Hadamard Manifolds

The KKT optimality conditions for multi-objective interval-valued optimization problem on Hadamard manifold are studied in this paper. Several concepts of Pareto optimal solutions, considered under LU and CW ordering on the class of all closed intervals in $\mathbb{R}$, are given. The KKT conditions are presented under the notions of convexity, pseudo-convexity and generalized Hukuhara difference. We show, with the help of an example, that the results done in this paper for solving multi-objective interval-valued optimization problems on Hadamard spaces are more general than the existing ones on Euclidean spaces. The main results are supported by examples.

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arXiv2023

Strongly geodesic preinvexity and Strongly Invariant η-Monotonicity on Riemannian Manifolds and its Application

In this paper, we present strongly geodesic preinvexity on Riemannian manifolds (RM) and strongly η-invexity of order m on RM. Furthermore, we define strongly invariant η-monotonicity of order m on RM. Under Condition C, an important characterization of these functions are studied. We construct several non-trivial examples in support of these definitions. Afterwords, an important and significant characterization of a strict η-minimizers (η-minimizers)of order m for MOP and a solution to the variational like-inequality problem (VVLIP) has been derived.

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