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＜電子ブック＞
Variable Ordering Structures in Vector Optimization / by Gabriele Eichfelder
(Vector Optimization. ISSN:1867898X)

版	1st ed. 2014.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XIII, 190 p. 41 illus : online resource
著者標目	*Eichfelder, Gabriele author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Operations research LCSH:Mathematics FREE:Optimization FREE:Operations Research and Decision Theory FREE:Applications of Mathematics FREE:Continuous Optimization
一般注記	1 Variable ordering structures -- 2 Optimality concepts and their characterization -- 3 Properties of cone-valued maps -- 4 Linear scalarizations -- 5 Nonlinear scalarizations -- 6 Scalarization for variable orderings given by Bishop-Phelps cones -- 7 Optimality conditions -- 8 Duality results -- 9 Numerical methods -- 10 Outlook and further application areas 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 HTTP:URL=https://doi.org/10.1007/978-3-642-54283-1

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