FPGA Implementation of Classical Dynamic Neural Networks for Smooth and Nonsmooth Optimization Problems

In this paper, a novel Field-Programmable-Gate-Array (FPGA) implementation framework based on Lagrange programming neural network (LPNN), projection neural network (PNN) and proximal projection neural network (PPNN) is proposed which can be used to solve smooth and nonsmooth optimization problems. First, Count Unit (CU) and Calculate Unit (CaU) are designed for smooth problems with equality constraints, and these units are used to simulate the iteration actions of neural network (NN) and form a feedback loop with other basic digital circuit operations. Then, the optimal solutions of optimization problems are mapped by the output waveforms. Second, the digital circuit structures of Path Select Unit (PSU), projection operator and proximal operator are further designed to process the box constraints and nonsmooth terms, respectively. Finally, the effectiveness and feasibility of the circuit are verified by three numerical examples on the Quartus II 13.0 sp1 platform with the Cyclone IV E series chip EP4CE10F17C8.