| RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS |
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| 引用本文： | 马儒宁,陈天平. RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS[J]. 应用数学和力学(英文版), 2006, 27(4): 543-554. DOI: 10.1007/s 10483-006-0415-z |
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| 作者姓名： | 马儒宁 陈天平 |
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| 作者单位： | Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016，P. R. China，Institute of Mathematics，Fudan University，Shanghai 200433，P. R. China，Institute of Mathematics Fudan University，Shanghai 200433，P. R. China |
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| 摘 要： | The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.
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| 关 键 词： | 循环神经网络模型 投影算子 优化问题 球形会聚 |
| 收稿时间： | 2004-03-24 |
| 修稿时间： | 2006-01-10 |
Recurrent neural network model based on projective operator and its application to optimization problems |
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| Ru-ning Ma Doctor,Tian-ping Chen. Recurrent neural network model based on projective operator and its application to optimization problems[J]. Applied Mathematics and Mechanics(English Edition), 2006, 27(4): 543-554. DOI: 10.1007/s 10483-006-0415-z |
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| Authors: | Ru-ning Ma Doctor Tian-ping Chen |
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| Affiliation: | 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, P. R. China;Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China
2. Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China |
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| Abstract: | The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN. |
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| Keywords: | recurrent neural network model projective operator global convergence optimization complementarity problems |
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