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Solving variational inequalities and...

Hu, Xiaolin.

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Solving variational inequalities and related problems using recurrent neural networks.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Solving variational inequalities and related problems using recurrent neural networks./
作者:	Hu, Xiaolin.
面頁冊數:	207 p.
附註:	Adviser: Jun Wang.
Contained By:	Dissertation Abstracts International69-02B.
標題:	Artificial Intelligence. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3302428
ISBN:	9780549483854

Solving variational inequalities and related problems using recurrent neural networks.
Hu, Xiaolin.

Solving variational inequalities and related problems using recurrent neural networks. - 207 p.

Adviser: Jun Wang.

Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2007.

Variational inequality (VI) can be viewed as a natural framework for unifying the treatment of equilibrium problems, and hence has applications across many disciplines. In addition, many typical problems are closely related to VI, including general VI (GVI), complementarity problem (CP), generalized CP (GCP) and optimization problem (OP).

ISBN: 9780549483854Subjects--Topical Terms:

769149
Artificial Intelligence.

Solving variational inequalities and related problems using recurrent neural networks.
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100 1 $a Hu, Xiaolin. $3 1282485
245 1 0 $a Solving variational inequalities and related problems using recurrent neural networks.
300 $a 207 p.
500 $a Adviser: Jun Wang.
500 $a Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1102.
502 $a Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2007.
520 $a Variational inequality (VI) can be viewed as a natural framework for unifying the treatment of equilibrium problems, and hence has applications across many disciplines. In addition, many typical problems are closely related to VI, including general VI (GVI), complementarity problem (CP), generalized CP (GCP) and optimization problem (OP).
520 $a During the past two decades, numerous recurrent neural networks (RNNs) have been proposed for solving VIs and related problems. However, first, the theories of many emerging RNNs have not been well founded yet; and their capabilities have been underestimated. Second, these RNNs have limitations in handling some types of problems. Third, it is certainly not true that these RNNs are best choices for solving all problems, and new network models with more favorable characteristics could be devised for solving specific problems.
520 $a In the research, the above issues are extensively explored from dynamic system perspective, which leads to the following major contributions. On one hand, many new capabilities of some existing RNNs have been revealed for solving VIs and related problems. On the other hand, several new RNNs have been invented for solving some types of these problems. The contributions are established on the following facts. First, two existing RNNs, called TLPNN and PNN, are found to be capable of solving pseudomonotone VIs and related problems with simple bound constraints. Second, many more stability results are revealed for an existing RNN, called GPNN, for solving GVIs with simple bound constraints, and it is then extended to solve linear VIs (LVIs) and generalized linear VIs (GLVIs) with polyhedron constraints. Third, a new RNN, called IDNN, is proposed for solving a special class of quadratic programming problems which features lower structural complexity compared with existing RNNs. Fourth, some local convergence results of an existing RNN, called EPNN, for nonconvex optimization are obtained, and two variants of the network by incorporating two augmented Lagrangian function techniques are proposed for seeking Karush-Kuhn-Tucker (KKT) points, especially local optima, of the problems.
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