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研究了一种基于投影算子的神经网络模型.与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同,而是n维欧氏空间中未必有界的闭凸子集,同时目标函数也是一般的连续可微函数,未必为凸函数.证明了所研究的神经网络模型具有整体解轨道,以及当日标函数满足某些条件时解轨道的整体收敛性.此外,还将所研究的模型应用于闭凸约束极小化问题以及非线性互补问题和隐互补问题中,并通过数值模拟说明了该神经网络方法的有效性.  相似文献   
2.
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.  相似文献   
3.
Let H be a separable Hilbert space and L(H) the set of all bounded linear operatorson H .A∈ L (H ) is said to be a contraction if‖ A‖≤ 1 .In [1 ] Sz-Nagy and Foiasintroduced the notion of the class Cαβ of contractions on H as follows: Definition1  Let T∈L(H) be a contraction.WriteT∈C0 .,   if h∈H,‖Tnh‖→ 0 ,as n→∞ ;T∈C1· ,  if h∈H,h≠ 0 ,‖ Tnh‖\→ 0 ,as n→∞ ;T∈C· 0 ,  if h∈H,‖ T* nh‖→ 0 ,as n→∞ ;T∈C· 1 ,  if h∈H,h≠ 0 ,‖ T* nh‖\→ 0 …  相似文献   
4.
Rn中连续算子的逼近问题的数值方法,一直是计算科学中研究的热点。本文引进了新兴的智能机器一支持向量机,以解决Rn中连续算子的逼近问题。在给出支持向量机用于算子逼近问题的详细数学表示之后,我们提出了分块逼近的算法,并通过具体的实例说明支持向量机在算子逼近问题中的有效性与优越性。  相似文献   
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