A Predefined-Time Neurodynamic Approach with Time-Varying Coefficients for Mixed Variational Inequalities and Applications

TL;DR

This paper introduces a predefined-time neurodynamic method with time-varying coefficients for efficiently solving mixed variational inequalities, ensuring convergence within a user-defined time frame.

Contribution

It develops a novel neurodynamic model with proven predefined-time stability and robustness, applicable to various optimization problems.

Findings

Guarantees convergence within a user-prescribed time

Proves robustness against bounded disturbances

Demonstrates fast convergence in numerical simulations

Abstract

This paper proposes a predefined-time (PDT) neurodynamic approach with time-varying coefficients for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models is developed to guarantee convergence within a user-prescribed time from arbitrary initial conditions. PDT stability is rigorously established via Lyapunov analysis under strong pseudomonotonicity and Lipschitz continuity assumptions, and explicit relationships between convergence time and system parameters are derived. The robustness of the proposed method against bounded disturbances is also analyzed. Applications to composite and minimax optimization problems, together with numerical simulations, demonstrate the effectiveness and fast convergence performance of the proposed framework.