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| Auteurs principaux: | , |
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| Format: | Preprint |
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2022
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| Accès en ligne: | https://arxiv.org/abs/2212.04541 |
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| _version_ | 1866916625039491072 |
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| author | Bhat, Hilal Ahmad Iqbal, Akhlad |
| author_facet | Bhat, Hilal Ahmad Iqbal, Akhlad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_04541 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalized Hukuhara directional differentiability of interval-valued functions on Riemannian manifolds Bhat, Hilal Ahmad Iqbal, Akhlad Optimization and Control Differential Geometry 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. |
| title | Generalized Hukuhara directional differentiability of interval-valued functions on Riemannian manifolds |
| topic | Optimization and Control Differential Geometry |
| url | https://arxiv.org/abs/2212.04541 |