Solving convex optimization problems using recurrent neural networks in finite time

A recurrent neural network is proposed to deal with the convex optimization problem. By employing a specific nonlinear unit, the proposed neural network is proved to be convergent to the optimal solution in finite time, which increases the computation efficiency dramatically. Compared with most of existing stability conditions, i.e., asymptotical stability and exponential stability, the obtained finite-time stability result is more attractive, and therefore could be considered as a useful supplement to the current literature. In addition, a switching structure is suggested to further speed up the neural network convergence. Moreover, by using the penalty function method, the proposed neural network can be extended straightforwardly to solving the constrained optimization problem. Finally, the satisfactory performance of the proposed approach is illustrated by two simulation examples.

I. Introduction

Recently, various engineering problems, such as the robot control, control system design, signal and image processing, and pattern recognition, can be converted into the optimization problems. However, traditional numerical algorithms for solving the optimization problems may encounter serious speed bottleneck due to the serial nature of the digital computer employed. Therefore, how to solve the optimization problem in real time has been studied intensively. One promising approach is to employ the artificial neural network based on the hardware implementation.