A novel gradient-based neural network for solving convex second-order cone constrained variational inequality problems

2019 ◽  
Vol 347 ◽  
pp. 343-356 ◽  
Author(s):  
Alireza Nazemi ◽  
Atiye Sabeghi
Keyword(s):  
Neural Network ◽  
Variational Inequality ◽  
Second Order ◽  
Variational Inequality Problems ◽  
Second Order Cone ◽  
Gradient Based

An Extended Projection Neural Network for Constrained Optimization

2004 ◽  
Vol 16 (4) ◽  
pp. 863-883 ◽  
Author(s):  
Youshen Xia
Keyword(s):  
Neural Network ◽  
Variational Inequality ◽  
Parallel Implementation ◽  
Variational Inequality Problems ◽  
Extended Projection ◽  
Linear And Nonlinear Constraints ◽  
Lower Complexity ◽  
Monotone Variational Inequality ◽  
Projection Neural Network ◽  
Special Case

Recently, a projection neural network has been shown to be a promising computational model for solving variational inequality problems with box constraints. This letter presents an extended projection neural network for solving monotone variational inequality problems with linear and nonlinear constraints. In particular, the proposed neural network can include the projection neural network as a special case. Compared with the modified projection-type methods for solving constrained monotone variational inequality problems, the proposed neural network has a lower complexity and is suitable for parallel implementation. Furthermore, the proposed neural network is theoretically proven to be exponentially convergent to an exact solution without a Lipschitz condition. Illustrative examples show that the extended projection neural network can be used to solve constrained monotone variational inequality problems.

scholarly journals Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Juhe Sun ◽  
Xiao-Ren Wu ◽  
B. Saheya ◽  
Jein-Shan Chen ◽  
Chun-Hsu Ko
Keyword(s):  
Neural Network ◽  
Second Order ◽  
Merit Functions ◽  
Second Order Cone ◽  
The Neural Network ◽  
Complementarity Functions ◽  
Type Classes ◽  
Quadratic Programming Problems ◽  
Numerical Performance ◽  
Discrete Type

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

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