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 o...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 205; H. 1; S. 6
Hauptverfasser: Bhat, Hilal Ahmad, Iqbal, Akhlad, Aftab, Mahwash
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2025
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Convex analysis
Decision making
Engineering
Euclidean space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization techniques
Random variables
Riemann manifold
Theory of Computation
Topological manifolds
Generalized Hukuhara directional derivative
Riemannian manifolds
Interval-valued functions
Convexity
KKT optimality conditions
ISSN:0022-3239, 1573-2878
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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 R .
AbstractList 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 R .
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 R.
ArticleNumber 6
Author Iqbal, Akhlad
Aftab, Mahwash
Bhat, Hilal Ahmad
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  surname: Aftab
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  organization: Department of Mathematics, Aligarh Muslim University
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Keywords Generalized Hukuhara directional derivative
Riemannian manifolds
Interval-valued functions
Convexity
KKT optimality conditions
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Snippet This article explores fundamental properties of convex interval-valued functions defined on Riemannian manifolds. The study employs generalized Hukuhara...
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SubjectTerms Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Convex analysis
Decision making
Engineering
Euclidean space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization techniques
Random variables
Riemann manifold
Theory of Computation
Topological manifolds
Title Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation
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