  We study the existence and uniqueness of solutions to the inverse
quasi-variational inequality problem. Motivated by the neural network approach
to solving optimization problems such as variational inequality, monotone
inclusion, and inverse variational problems, we consider a neural network
associated with the inverse quasi-variational inequality problem, and establish
the existence and uniqueness of a solution to the proposed network. We prove
that every trajectory of the proposed neural network converges to the unique
solution of the inverse quasi-variational inequality problem and that the
network is globally asymptotically stable at its equilibrium point. We also
prove that if the function which governs the inverse quasi-variational
inequality problem is strongly monotone and Lipschitz continuous, then the
network is globally exponentially stable at its equilibrium point. We
discretize the network and show that the sequence generated by the
discretization of the network converges strongly to a solution of the inverse
quasi-variational inequality problem under certain assumptions on the
parameters involved. Finally, we provide numerical examples to support and
illustrate our theoretical results.
