A New One-Layer Neural Network for Linear and Quadratic Programming
In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective f...
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| Vydané v: | IEEE transactions on neural networks Ročník 21; číslo 6; s. 918 - 929 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
IEEE
01.06.2010
Institute of Electrical and Electronics Engineers |
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| ISSN: | 1045-9227, 1941-0093, 1941-0093 |
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| Abstract | In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results. |
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| AbstractList | In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results. In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results. |
| Author | Li-Zhi Liao Xingbao Gao |
| Author_xml | – sequence: 1 surname: XINGBAO GAO fullname: XINGBAO GAO organization: College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China – sequence: 2 givenname: Li-Zhi surname: LIAO fullname: LIAO, Li-Zhi organization: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong-Kong |
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| Keywords | Transient response linear and quadratic programming Lyapunov method Linear programming Neural network Quadratic programming Real time Modeling Transients Exact solution Convergence Neuron Optimal solution Equality constraint Convex function Objective function stability Lyapunov function |
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| SubjectTerms | Applied sciences Artificial intelligence Artificial neural networks Computer networks Computer science; control theory; systems Computer Simulation Connectionism. Neural networks Convergence Design optimization Exact sciences and technology Humans linear and quadratic programming Linear programming Mathematical analysis Mathematical programming Mathematics neural network Neural networks Neural Networks (Computer) Neurons Nonlinear Dynamics Operational research and scientific management Operational research. Management science Optimization Programming, Linear Quadratic programming Real time Stability Vectors Vectors (mathematics) |
| Title | A New One-Layer Neural Network for Linear and Quadratic Programming |
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