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

Hilal Ahmad Bhat (), Akhlad Iqbal () and Mahwash Aftab ()
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Hilal Ahmad Bhat: Aligarh Muslim University
Akhlad Iqbal: Aligarh Muslim University
Mahwash Aftab: Aligarh Muslim University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 6, 29 pages

Abstract: Abstract 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 the type of functions involved in optimization problems, we consider the following cases: objective function as well as constraints are real-valued; objective function is interval-valued and constraints are real-valued; 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 $$\mathbb {R}$$ R .

Keywords: KKT optimality conditions; Generalized Hukuhara directional derivative; Interval-valued functions; Riemannian manifolds; Convexity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02618-3

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