A Novel Recurrent Neural Network for Solving Nonlinear Optimization Problems With Inequality Constraints

This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush...

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Bibliographic Details
Published in:IEEE transactions on neural networks Vol. 19; no. 8; pp. 1340 - 1353
Main Authors: Xia, Youshen, Feng, Gang, Wang, Jun
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2008
Institute of Electrical and Electronics Engineers
Subjects:
Algorithms
Application software
Applied sciences
Artificial Intelligence
Computer science; control theory; systems
Computer Simulation
Computer systems and distributed systems. User interface
Connectionism. Neural networks
Constraint optimization
Constraints
Convergence
Design engineering
Exact sciences and technology
Global convergence
Inequalities
Lagrangian functions
Linear matrix inequalities
Linear programming
Models, Theoretical
Neural networks
Neural Networks (Computer)
nonconvex programming
Nonlinear Dynamics
nonlinear inequality constraints
Nonlinearity
nonsmooth analysis
Optimization
Pattern Recognition, Automated - methods
Projection
recurrent neural network
Recurrent neural networks
Software
Very large scale integration
Recurrent neural nets
nonlinear inequality constraints
Non convex programming
Global convergence
Lagrangian
recurrent neural network
Lyapunov method
nonconvex programming
Nonlinear problems
Non linear programming
Network management
Neural network
Convex programming
Constrained optimization
nonsmooth analysis
Inequality constraint
Kuhn Tucker method
Hessian matrices
Non convex analysis
Lyapunov function
Mathematical programming
ISSN:1045-9227, 1941-0093, 1941-0093
Online Access:Get full text
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Summary:This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush-Kuhn-Tucker point in the sense of Lyapunov and its output trajectory is globally convergent to a minimum solution. Compared with variety of the existing projection neural networks, including their extensions and modification, for solving such nonlinearly constrained optimization problems, it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point. Simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems.
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SourceType-Scholarly Journals-1
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ISSN:1045-9227
1941-0093
1941-0093
DOI:10.1109/TNN.2008.2000273