On relationships between vector variational inequalities and optimization problems using convexificators on the Hadamard manifold
This study extended a fundamental idea about convexificators to the Hadamard manifolds. The mean value theorem for convexificators on the Hadamard manifold was also derived. An important characterization for the bounded convexificators to have $ \partial_{*}^{*} $-geodesic convexity was derived and...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025259 |
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| Summary: | This study extended a fundamental idea about convexificators to the Hadamard manifolds. The mean value theorem for convexificators on the Hadamard manifold was also derived. An important characterization for the bounded convexificators to have $ \partial_{*}^{*} $-geodesic convexity was derived and the monotonicity of the bounded convexificators was explored. Additionally, a convexificator-based vector variational inequality problem on the Hadamard manifold was examined. Furthermore, the necessary and sufficient conditions for vector optimization problems in terms of the Stampacchia and Minty-type partial vector variational inequality problems ($ \partial_{*}^{*} $-VVIPs) were derived. |
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| ISSN: | 2473-6988 |