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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Bibliographic Details
Main Authors: Nagendra Singh, Sunil Kumar Sharma, Akhlad Iqbal, Shahid Ali
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:AIMS Mathematics
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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.
ISSN:2473-6988