A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems

In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisf...

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Bibliographic Details
Published inIEEE transactions on neural networks Vol. 19; no. 10; pp. 1665 - 1677
Main Authors Barbarosou, M.P., Maratos, N.G.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.10.2008
Institute of Electrical and Electronics Engineers
Subjects
Algorithms
Applied sciences
Artificial intelligence
Circuits
Computer science; control theory; systems
Computer Simulation
Connectionism. Neural networks
Constrained optimization
Constraint optimization
Convergence
convex and nonconvex problems
Design optimization
Exact sciences and technology
Feedback
Lagrangian functions
Models, Theoretical
Neural networks
Neural Networks (Computer)
Nonlinear equations
Numerical Analysis, Computer-Assisted
Piecewise linear techniques
Programming profession
Recurrent neural networks
Exponential convergence
Recurrent neural nets
Non convex programming
convergence
convex and nonconvex problems
Constraint satisfaction
Network management
Neural network
Convex programming
Constrained optimization
recurrent neural networks
Convergence rate
Convexity
Numerical convergence
Non convex analysis
Mathematical programming
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ISSN1045-9227
1941-0093
1941-0093
DOI10.1109/TNN.2008.2000993

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Summary:In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t rarr infin. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate.
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ISSN:1045-9227
1941-0093
1941-0093
DOI:10.1109/TNN.2008.2000993