Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915165507682304 |
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| author | Bhat, Hilal Ahmad Iqbal, Akhlad Aftab, Mahwash |
| author_facet | Bhat, Hilal Ahmad Iqbal, Akhlad Aftab, Mahwash |
| contents | 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 $\mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation Bhat, Hilal Ahmad Iqbal, Akhlad Aftab, Mahwash Optimization and Control Differential Geometry 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 $\mathbb{R}$. |
| title | Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation |
| topic | Optimization and Control Differential Geometry |
| url | https://arxiv.org/abs/2309.09396 |