Neurodynamic optimization approaches with finite/fixed-time convergence for absolute value equations

This paper proposes three novel accelerated inverse-free neurodynamic approaches to solve absolute value equations (AVEs). The first two are finite-time converging approaches and the third one is a fixed -time converging approach. It is shown that the proposed first two neurodynamic approaches converge to the solution of the concerned AVEs in a finite-time while, under some mild conditions, the third one converges to the solution in a fixed-time. It is also shown that the settling time for the proposed fixed-time converging approach has an uniform upper bound for all initial conditions, while the settling times for the proposed finite-time converging approaches are dependent on initial conditions. The proposed neurodynamic approaches have the advantage that they are all robust against bounded vanishing perturbations. The theoretical results are validated by means of a numerical example and an application in boundary value problems.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes three novel accelerated inverse-free neurodynamic approaches to solve absolute value equations. The first two approaches converge in a finite-time, while the third approach converges in a fixed-time. It is shown that the proposed methods converge to the solution of the absolute value equations, and the settling times depend on initial conditions. The robustness of the proposed approaches against bounded vanishing perturbations is also demonstrated. The theoretical results are validated through numerical examples and applications in boundary value problems.