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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Vydáno v:	IEEE transactions on neural networks Ročník 19; číslo 8; s. 1340 - 1353
Hlavní autoři:	Xia, Youshen, Feng, Gang, Wang, Jun
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.08.2008 Institute of Electrical and Electronics Engineers
Témata:	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
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1045-9227 1941-0093 1941-0093
DOI:	10.1109/TNN.2008.2000273