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Titlebook: Duality Principles in Nonconvex Systems; Theory, Methods and David Yang Gao Book 2000 Springer Science+Business Media Dordrecht 2000 Mathe

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发表于 2025-3-21 20:04:26 | 显示全部楼层 |阅读模式
书目名称Duality Principles in Nonconvex Systems
副标题Theory, Methods and
编辑David Yang Gao
视频video
丛书名称Nonconvex Optimization and Its Applications
图书封面Titlebook: Duality Principles in Nonconvex Systems; Theory, Methods and  David Yang Gao Book 2000 Springer Science+Business Media Dordrecht 2000 Mathe
描述Motivated by practical problems in engineering and physics,drawing on a wide range of applied mathematical disciplines, this bookis the first to provide, within a unified framework, a self-containedcomprehensive mathematical theory of duality for general non-convex,non-smooth systems, with emphasis on methods and applications inengineering mechanics. Topics covered include the classical (minimax)mono-duality of convex static equilibria, the beautiful bi-duality indynamical systems, the interesting tri-duality in non-convex problemsand the complicated multi-duality in general canonical systems. Apotentially powerful sequential canonical dual transformation methodfor solving fully nonlinear problems is developed heuristically andillustrated by use of many interesting examples as well as extensiveapplications in a wide variety of nonlinear systems, includingdifferential equations, variational problems and inequalities,constrained global optimization, multi-well phase transitions,non-smooth post-bifurcation, large deformation mechanics, structurallimit analysis, differential geometry and non-convex dynamicalsystems. .With exceptionally coherent and lucid exposition, the work fills a bi
出版日期Book 2000
关键词Mathematica; applied mathematics; deformation; dynamical systems; engineering mechanics; functional analy
版次1
doihttps://doi.org/10.1007/978-1-4757-3176-7
isbn_softcover978-1-4419-4825-0
isbn_ebook978-1-4757-3176-7Series ISSN 1571-568X
issn_series 1571-568X
copyrightSpringer Science+Business Media Dordrecht 2000
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发表于 2025-3-21 22:32:21 | 显示全部楼层
Book 2000al problems and inequalities,constrained global optimization, multi-well phase transitions,non-smooth post-bifurcation, large deformation mechanics, structurallimit analysis, differential geometry and non-convex dynamicalsystems. .With exceptionally coherent and lucid exposition, the work fills a bi
发表于 2025-3-22 03:02:20 | 显示全部楼层
发表于 2025-3-22 04:48:20 | 显示全部楼层
发表于 2025-3-22 09:53:38 | 显示全部楼层
Duality in Geometrically Linear Systemsrecent monograph by Motreanu and Panagiotopoulos (1999) for details. However, readers who is not interested in these mathematical details can certainly omit this chapter and continue to the next chapter without difficulty.
发表于 2025-3-22 13:52:37 | 显示全部楼层
Tri-Duality in Nonconvex Systemsy relation no longer exists. The solutions in these systems are usually not unique. But, by introducing a suitable nonlinear operator A, a generalized framework may still be established for many systems. The resulting triality theory reveals interesting local dualities (see Fig. 3.1, the associated problem is given in Example 3.3).
发表于 2025-3-22 19:11:44 | 显示全部楼层
Multi-Duality and Classifications of General Systemssystems and a generalized tri-duality principle is presented in the central part of this section, which plays a core role in this book. Examples from discrete systems and continuum fields are listed. We end up by giving an application for nonconvex systems.
发表于 2025-3-22 22:18:25 | 显示全部楼层
Book 2000de, within a unified framework, a self-containedcomprehensive mathematical theory of duality for general non-convex,non-smooth systems, with emphasis on methods and applications inengineering mechanics. Topics covered include the classical (minimax)mono-duality of convex static equilibria, the beaut
发表于 2025-3-23 04:45:14 | 显示全部楼层
Innovating: Humans Are Ingenious Animals,y relation no longer exists. The solutions in these systems are usually not unique. But, by introducing a suitable nonlinear operator A, a generalized framework may still be established for many systems. The resulting triality theory reveals interesting local dualities (see Fig. 3.1, the associated problem is given in Example 3.3).
发表于 2025-3-23 08:11:23 | 显示全部楼层
Aggregating: Humans Are Social Animals,systems and a generalized tri-duality principle is presented in the central part of this section, which plays a core role in this book. Examples from discrete systems and continuum fields are listed. We end up by giving an application for nonconvex systems.
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