@article{Singh2025, 
author = {Nagendra Singh and Sunil Kumar Sharma and Akhlad Iqbal and Shahid Ali},
title = {On relationships between vector variational inequalities and optimization problems using convexificators on the Hadamard manifold},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5612-5630},
keywords = {geodesic convexity, monotonicity, ∂∗∗-VVIP, VOP, Hadamard manifold},
url = {https://www.sciopen.com/article/10.3934/math.2025259},
doi = {10.3934/math.2025259},
abstract = {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        ∂          ∗              ∗      -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 (       ∂          ∗              ∗      -VVIPs) were derived.}
}