Fixed-time neural networks with time-invariant and time-varying coefficients for mixed variational inequalities

This paper develops several fixed -time neural networks for solving mixed variational inequalities (MVIs). The proposed networks are highly efficient and with fixed -time convergence. First, based on the conventional forward -backward -forward neural network (FNN) and sliding mode control technique, a time -invariant fixed -time FNN (FxTFNN) is designed. Next, the Euclidean norm of FNN is introduced into FxTFNN to design the modified FxTFNN (MFxTFNN). It is shown that the proposed FxTFNN and MFxTFNN have fixed -time convergence properties and their settling -time functions are independent of the initial values. The proposed FxTFNN and MFxTFNN can be used to solve the Lasso problem and apply sparse signal reconstruction and image reconstruction. In addition, by introducing time -varying coefficients based on FxTFNN and MFxTFNN, timevarying FxTFNN (TFxTFNN) and time -varying MFxTFNN (TMFxTFNN) are developed. Finally, experimental results of numerical example, signal reconstruction, and image reconstruction are used to verify the effectiveness and superiority of the proposed neural networks.