Fixed-Time Convergence of Time-Varying Neurodynamic Systems for Mixed Variational Inequalities

TL;DR

This paper introduces fixed-time convergent neurodynamic models for solving mixed variational inequalities, ensuring rapid convergence from any initial condition with robustness to disturbances.

Contribution

It develops novel time-varying proximal neurodynamic models with fixed-time convergence guarantees and explicit bounds on settling time.

Findings

Models achieve fixed-time convergence from arbitrary initial conditions.

Explicit upper bounds on convergence time are derived.

Numerical examples demonstrate effectiveness and robustness.

Abstract

This paper proposes novel fixed-time (FXT) convergent neurodynamic approaches for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models (PNMs), including time-varying proximal neurodynamic models (TVPNMs), is developed to guarantee FXT convergence to the solution of MVIs from arbitrary initial conditions. Rigorous convergence and stability analyses are established under the assumptions of strong pseudomonotonicity and Lipschitz continuity, using Lyapunov stability theory. The proposed methods exhibit FXT convergence from any initial point, with convergence speed significantly enhanced through the strategic design of time-varying coefficients. Explicit upper bounds on the settling time are derived for the time-varying neurodynamic models. In addition, the robustness of the proposed approaches against bounded noise disturbances is analyzed. The applicability of the proposed framework is further demonstrated for composite optimization problems and minimax optimization problems. Also, numerical examples are presented to demonstrate the effectiveness and convergence behavior of the proposed methods.