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 ${\mathrm{\partial }}_{\ast }^{\ast }$-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 ( ${\mathrm{\partial }}_{\ast }^{\ast }$-VVIPs) were derived.