A Smoothing Neural Network Algorithm for Absolute Value Equations

Abstract

In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.

In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.

Keywords

Absolute Value Equations, Neural Network, Smoothing Function, Linear Complementarity Problem

Absolute Value Equations, Neural Network, Smoothing Function, Linear Complementarity Problem

Cite this paper

Wang, F. , Yu, Z. and Gao, C. (2015) A Smoothing Neural Network Algorithm for Absolute Value Equations.*Engineering*, **7**, 567-576. doi: 10.4236/eng.2015.79052.

Wang, F. , Yu, Z. and Gao, C. (2015) A Smoothing Neural Network Algorithm for Absolute Value Equations.

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