  In this paper, a novel modified proximal dynamical system is proposed to
compute the solution of a mixed variational inequality problem (MVIP) within a
fixed time, where the time of convergence is finite and is uniformly bounded
for all initial conditions. Under the assumptions of strong monotonicity and
Lipschitz continuity, it is shown that a solution of the modified proximal
dynamical system exists, is uniquely determined, and converges to the unique
solution of the associated MVIP within a fixed time. Furthermore, the
fixed-time stability of the modified projected dynamical system continues to
hold, even if the assumption of strong monotonicity is relaxed to that of
strong pseudomonotonicity. Finally, it is shown that the solution obtained
using the forward-Euler discretization of the proposed modified proximal
dynamical system converges to an arbitrarily small neighborhood of the solution
of the associated MVIP within a fixed number of time steps, independent of the
initial conditions.
