A neurodynamic approach with fixed-time convergence for complex-variable pseudo-monotone variational inequalities

Abstract

Based on Wirtinger calculus, this paper proposes a complex-valued projection neural network (CPNN) designed to address complex-variables variational inequality problems. The global convergence of the CPNN is established under the assumptions of pseudomonotonicity and Lipschitz continuity. We demonstrate that the CPNN achieves convergence within a fixed-time, which is unaffected by the initial conditions and converges towards the optimal solution of the constrained optimization problem. And this result is distinct from asymptotic or exponential convergence that depend on initial condition. Furthermore, the CPNN shows utility in tackling diverse related problems, encompassing variational inequalities, pseudo-convex optimization problems, linear and nonlinear complementarity problems, as well as linear and convex quadratic programming problems. The efficacy of the proposed CPNN is substantiated through numerical simulations.