Fixed-time neurodynamic optimization approach with time-varying coefficients to variational inequality problems and applications

The article presents a novel fixed-time (FT) neurodynamic optimization approach featuring time-varying coefficients, tailored for variational inequality problems (VIPs). This method exhibits noteworthy properties, including FT convergence from any initial point, accelerated by the strategic selection of time-varying coefficients. Detailed upper bounds on the settling time for the time-varying neurodynamic approach are provided. Additionally, the article delves into the robustness of the neurodynamic approach against bounded noise disturbances. Three implementation ways by numerical discretization, analog circuits, and field-programmable gate array (FPGA) of the proposed FT neurodynamic optimization approach are demonstrated. Finally, two applications on Nash equilibrium seeking problems and image recovery are conducted to validate the practicability and superiority of the proposed time-varying neurodynamic approach. © 2024 Elsevier B.V.