Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalitie...

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Veröffentlicht in:IEEE transactions on neural networks Jg. 17; H. 6; S. 1487 - 1499
Hauptverfasser: Hu, Xiaolin, Wang, Jun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.11.2006
Institute of Electrical and Electronics Engineers
Schlagworte:
Algorithms
Applied sciences
Artificial intelligence
Artificial neural networks
Asymptotic properties
Asymptotic stability
Circuits
Componentwise pseudomonotone variational inequality
Computer science; control theory; systems
Connectionism. Neural networks
Constraint optimization
Constraints
Convergence
Exact sciences and technology
global asymptotic stability
Inequalities
Information Storage and Retrieval - methods
Iterative algorithms
Neural networks
Neural Networks (Computer)
Optimization
Pattern Recognition, Automated - methods
Projection
projection neural network
pseudoconvex optimization
pseudomonotone variational inequality
Recurrent neural networks
Signal processing algorithms
Signal Processing, Computer-Assisted
Stability
Telecommunication traffic
Monotonic function
Recurrent neural nets
Componentwise pseudomonotone variational inequality
global asymptotic stability
pseudoconvex optimization
Lyapunov method
Neural network
Convex programming
Constrained optimization
projection neural network
Asymptotic stability
Variational inequality
pseudomonotone variational inequality
Monotonicity
Lyapunov function
Mathematical programming
ISSN:1045-9227, 1941-0093
Online-Zugang:Volltext
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Zusammenfassung:In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network
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ISSN:1045-9227
1941-0093
DOI:10.1109/TNN.2006.879774