Applications of Recurrent Neural Networks to Optimization Problems

Abstract

The work in this chapter presents some applications of recurrent neural networks to general optimization problems. While particular problems presented in this research relates to linear, quadratic and nonlinear programming, monotone variational inequalities and complementarity problems, I fell that the methodology by which one solves these problems are quite general and warrants attention in and of themselves. Correspondingly, I hope that this material will be taken as both a response to a particular problem and a general method. Constrained optimization problems are defined as the mathematical representation of real world problems concerned with the determination of a minimum or a maximum of a function of several variables, which are required to satisfy a number of constraints. Such function optimization are sought in diverse fields, including mechanical, electrical and industrial engineering, operational research, management sciences, computer sciences, system analysis, economics, medical sciences, manufacturing, social and public planning and image processing. Although many classical optimization algorithms such as simplex, Karmarkar interior point, direct and indirect techniques are given to solve linear, quadratic and nonlinear optimization problems, in many applications, it is desire to have real-time on-line solutions of corresponding optimization problems. However, traditional optimization algorithms are not suitable for real-time on-line implementation on the computer. The dynamical system approach is one of the promising approaches that can handle these difficulties. In the recent years many artificial neural networks models developed to solve optimization problems. Several basic and advance questions associated with these models have motivated the studies presented in this chapter. The goal of this chapter is twofold. The theoretical areas of interest include fundamental methods, models and algorithms for solving general optimization problems using artificial recurrent neural networks. On the other hand, it will try to present and discuss the numerical analysis for the corresponding models, simulations and applications of recurrent neural networks that solve various practical optimization problems. Recurrent dynamical neural network is an area of neural networks which is one of the fundamental topics of the subject, and combines many mathematical concepts like ordinary and partial differential equations, dynamical systems, unconstrained and constrained O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m