Constrained optimization problems arise widely in scientific research and engineering applications. In the past two decades, solving optimization problems using recurrent neural network methods have been extensively investigated due to the advantages of massively parallel operations and rapid convergence. In real applications, neural networks with simple architecture and good performance are desired. However, most existing neural networks have some limitations and disadvantages in the convergence conditions or architecture complexity. This thesis is concentrated on analysis and design of recurrent neural networks with simplified architecture but for solving more general convex optimization problems. In this thesis, some improved recurrent neural networks have been proposed for solving smooth and non-smooth convex optimization problems and applied to some selected applications. / In Part I, we first propose a one-layer recurrent neural network for solving linear programming problems. Compared with other neural networks for linear programming, the proposed neural network has simpler architecture and better convergence properties. Second, a one-layer recurrent neural network is proposed for solving quadratic programming problems. The global convergence of the neural network can be guaranteed if only the objective function of the programming problem is convex on the equality constraints and not necessarily convex everywhere. Compared with the other neural networks for quadratic programming, such as the Lagrangian network and projection neural network, the proposed neural network has simpler architecture which neurons is the same as the number of the optimization problems. Third, combining the projection and penalty parameter methods, a one-layer recurrent neural network is proposed for solving general convex optimization problems with linear constraints. / In Part II, some improved recurrent neural networks are proposed for solving non-smooth convex optimization problems. We first proposed a one-layer recurrent neural network for solving the non-smooth convex programming problems with only equality constraints. This neural network simplifies the Lagrangian network and extend the neural network to solve non-smooth convex optimization problems. Then, a two-layers recurrent neural network is proposed for the non-smooth convex optimization subject to linear equality and bound constraints. / In Part III, some selected applications of the proposed neural networks are also discussed. The k-winners-take-all (kWTA) operation is first converted to equivalent linear and quadratic optimization problems and two kWTA network models are tailed to do the kWTA operation. Then, the proposed neural networks are applied to some other problems, such as the linear assignment, support vector machine learning and curve fitting problems. / Liu, Qingshan. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3606. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 133-145). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344316 |
| Date | January 2008 |
| Contributors | Liu, Qingshan., Chinese University of Hong Kong Graduate School. Division of Automation and Computer-Aided Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (xiv, 147 leaves : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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