A class of differential vector variational inequalities in finite dimensional spaces (Q467459)

Inspired by the work of \textit{J.-S. Pang} and \textit{D. E. Stewart} [Math. Program. 113, No. 2 (A), 345--424 (2008; Zbl 1139.58011)], the authors introduce differential vector variational inequalities in finite dimensional Euclidean spaces. The relationship between differential vector variational inequalities and differential scalar variational inequalities is studied. They establish some results on existence and linear growth of solutions to scalar variational inequalities. In particular, they prove existence theorems for Carathéodory weak solutions of differential vector variational inequalities. A convergence result on the Euler time-dependent procedure for solving initial-value differential vector variational inequalities is studied.