Neural networks for solving second-order cone constrained variational inequality problem

Authors:
Juhe Sun;Jein-Shan Chen;Chun-Hsu Ko
Affiliations:
School of Science, Shenyang Aerospace University, Shenyang, China 110136;Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677;Department of Electrical Engineering, I-Shou University, Kaohsiung, Taiwan 840
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.