A Novel Fixed-Time Converging Neurodynamic Approach to Mixed Variational Inequalities and Applications

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.