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Titlebook: Variable Ordering Structures in Vector Optimization; Gabriele Eichfelder Book 2014 Springer-Verlag Berlin Heidelberg 2014 cone-valued maps

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發(fā)表于 2025-3-21 19:56:49 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Variable Ordering Structures in Vector Optimization
編輯Gabriele Eichfelder
視頻videohttp://file.papertrans.cn/981/980511/980511.mp4
概述Presents variable ordering structures for the first time in book length format.Includes applications in Economics and Health.Provides algorithms for solving finite discrete as well as continuous vecto
叢書名稱Vector Optimization
圖書封面Titlebook: Variable Ordering Structures in Vector Optimization;  Gabriele Eichfelder Book 2014 Springer-Verlag Berlin Heidelberg 2014 cone-valued maps
描述This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
出版日期Book 2014
關(guān)鍵詞cone-valued maps; duality; linear scalarization; nonlinear scalarization; numerical methods; optimality c
版次1
doihttps://doi.org/10.1007/978-3-642-54283-1
isbn_softcover978-3-662-52551-7
isbn_ebook978-3-642-54283-1Series ISSN 1867-8971 Series E-ISSN 1867-898X
issn_series 1867-8971
copyrightSpringer-Verlag Berlin Heidelberg 2014
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發(fā)表于 2025-3-21 23:00:15 | 只看該作者
Variable Ordering Structures in Vector Optimization978-3-642-54283-1Series ISSN 1867-8971 Series E-ISSN 1867-898X
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發(fā)表于 2025-3-22 02:53:37 | 只看該作者
Cone-Valued Maps,amine classical properties, formerly introduced for arbitrary set-valued maps, like convexity, cone-convexity, linearity or monotonicity. It turns out that some of these properties like convexity directly imply that the cone-valued map is constant. In case of non-appropriateness of the classical notions we propose new concepts
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Outlook and Further Application Areas,rity and equilibrium problems. We show that the theory of consumer demand in economics is also related to variable ordering structures. Finally, we discuss an application in the treatment planning in intensity-modulated radiation therapy.
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發(fā)表于 2025-3-23 01:07:44 | 只看該作者
Variable Ordering Structures,In this chapter we recall basic concepts of partially ordered spaces and basic results on ordering cones and dual cones. We introduce variable ordering structures and examine their properties. We also focus on special ordering maps where the images are Bishop-Phelps cones and discuss several applications.
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