A Fixed-Time Proximal Gradient Neurodynamic Network With Time-Varying Coefficients for Composite Optimization Problems and Sparse Optimization Problems With Log–Sum Function

This article presents a novel proximal gradient neurodynamic network (PGNN) for solving composite optimization problems (COPs). The proposed PGNN with time-varying coefficients can be flexibly chosen to accelerate the network convergence. Based on PGNN and sliding mode control technique, the proposed time-varying fixed-time proximal gradient neurodynamic network (TVFxPGNN) has fixed-time stability and a settling time independent of the initial value. It is further shown that fixed-time convergence can be achieved by relaxing the strict convexity condition via the Polyak-Lojasiewicz condition. In addition, the proposed TVFxPGNN is being applied to solve the sparse optimization problems with the log–sum function. Furthermore, the field-programmable gate array (FPGA) circuit framework for time-varying fixed-time PGNN is implemented, and the practicality of the proposed FPGA circuit is verified through an example simulation in Vivado 2019.1. Simulation and signal recovery experimental results demonstrate the effectiveness and superiority of the proposed PGNN.