A Noise-Tolerant Proximal Neurodynamic Algorithm for Solving MVIPs in Fixed-Time With Circuit Implementations and Applications

In this paper, we propose a new noise-tolerant neurodynamic algorithm with fixed-time convergence to solve mixed variational inequality problems (MVIPs) and design the circuit framework for its hardware implementation. We prove that the proposed neurodynamic algorithm converges to a unique solution within fixed-time under some conditions and give its convergence time upper bound, which is independent of the initial states. Meanwhile, the robustness of the neurodynamic algorithm under additive perturbations is also demonstrated. In addition, the proposed neurodynamic algorithm is implemented using numerical simulation, analog circuits, and field-programmable gate array (FPGA) respectively. Finally, the superiority of the proposed algorithm is verified by two applications of image reconstruction and elastic net logistic regression.

I. Introduction

MVIPs constitute a typical class of problems in both mathematics and economics, which have been applied across diverse real-world scenarios, such as pricing in a power-transportation coupled network [1], ampere-volt characteristics for circuits [2] and redundant robot manipulators [3]. Mixed variational inequality provides a framework for studying optimization problems in the presence of constraints, especially when there are interactions or competitions among decision variables, allowing for a more accurate description of complex systems involving various types of constraints such as equations, and set constraints [4], [5], [6].