Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks
Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks
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DOI：
10.1109/tnn.2007.899753
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发表时间：
2007-11
影响因子：
--
通讯作者：
Xiaolin Hu;Jun Wang
中科院分区：
文献类型：
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作者：
Xiaolin Hu;Jun Wang
广义线性变分不等式(GLVI)是典型线性变分不等式的推广。近年来，一种被称为广义投影神经网络的递归神经网络被发展起来，用于求解具有简单边界(通常是箱型或球型)约束的GLVI。本文的目的是双重的。首先，给出了广义神经网络稳定性的一些进一步结果。其次，对广义神经网络进行了扩展，使其适用于求解一般线性等式和不等式约束的广义LVI问题。在此基础上，提出了一种新的GPNN设计方法。此外，针对不同类型的约束，讨论了减少GPNN神经元数目的方法，从而得到两个特定的GPNN。此外，基于其特殊的结构，还探讨了所得到的GPNN的一些独特的性质。给出了数值模拟结果，验证了结果的正确性。
Generalized linear variational inequality (GLVI) is an extension of the canonical linear variational inequality. In recent years, a recurrent neural network (NN) called general projection neural network (GPNN) was developed for solving GLVIs with simple bound (often box-type or sphere-type) constraints. The aim of this paper is twofold. First, some further stability results of the GPNN are presented. Second, the GPNN is extended for solving GLVIs with general linear equality and inequality constraints. A new design methodology for the GPNN is then proposed. Furthermore, in view of different types of constraints, approaches for reducing the number of neurons of the GPNN are discussed, which results in two specific GPNNs. Moreover, some distinct properties of the resulting GPNNs are also explored based on their particular structures. Numerical simulation results are provided to validate the results.