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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Communicated by LIU Zeng-rong
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Ma, Rn., Chen, Tp. Recurrent neural network model based on projective operator and its application to optimization problems. Appl Math Mech 27, 543–554 (2006). https://doi.org/10.1007/s10483-006-0415-z
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DOI: https://doi.org/10.1007/s10483-006-0415-z
Key words
- recurrent neural network model
- projective operator
- global convergence
- optimization
- complementarity problems