On vector quasivariational inequalities

In this paper, we consider the vector quasivariational inequalities and the vector quasivariational-like inequalities for multifunctions with vector values and prove some existence theorems of solutions for our inequalities. Also, we give the relationship between a kind of the vector variational inequality for multifunctions and a vector optimization problem involving nondifferentiable Lipschitz functions. (C) 1996 Academic Press, Inc.