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Vector Optimization

Scalarization and Separation by Translation Invariant Functions

with Applications in Optimization, Nonlinear Functional Analysis, and Mathematical Economics

Authors: Tammer, Christiane, Weidner, Petra

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  • The first monograph on translation invariant functions
  • Includes applications from vector optimization, set-valued optimization and optimization under uncertainty
  • Presents examples from mathematical finance, consumer and production theory
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eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-030-44723-6
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Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-030-44721-2
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About this book

Like norms, translation invariant functions are a natural and powerful tool for the separation of sets and scalarization. This book provides an extensive foundation for their application. It presents in a unified way new results as well as results which are scattered throughout the literature. The functions are defined on linear spaces and can be applied to nonconvex problems. Fundamental theorems for the function class are proved, with implications for arbitrary extended real-valued functions. The scope of applications is illustrated by chapters related to vector optimization, set-valued optimization, and optimization under uncertainty, by fundamental statements in nonlinear functional analysis and by examples from mathematical finance as well as from consumer and production theory. 

The book is written for students and researchers in mathematics and mathematical economics. Engineers and researchers from other disciplines can benefit from the applications, for example from scalarization methods for multiobjective optimization and optimal control problems.

About the authors

Christiane Tammer is Professor at Martin-Luther-University Halle-Wittenberg in Halle (Saale), Gemany. She is working in the field of variational analysis and optimization. She has co-authored four monographs: Set-Valued Optimization - An Introduction with Applications (Springer 2015), Variational Methods in Partially Ordered Spaces (Springer 2003), Angewandte Funktionalanalysis (Vieweg+Teubner  2009),  Approximation und Nichtlineare Optimierung in Praxisaufgaben (Springer 2017). She is Editor in Chief of the journal Optimization, Co-Editor in Chief of the journal Applied Set-Valued Analysis and Optimization and a member of the Editorial Board of several journals, the Scientific Committee of the Working Group on Generalized Convexity and EUROPT Managing Board.

Petra Weidner is Professor for Mathematics and Computer Science at HAWK University of Applied Sciences and Arts Hildesheim/Holzminden/Göttingen in Göttingen, Germany. She has worked at Martin-Luther-University Halle-Wittenberg and University Hamburg as well as for a business consulting firm. Her research interests include fundamentals of nonlinear functional analysis, operations research, vector optimization and decision making as well as solution methods for multiobjective optimization problems.


Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-030-44723-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-030-44721-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Scalarization and Separation by Translation Invariant Functions
Book Subtitle
with Applications in Optimization, Nonlinear Functional Analysis, and Mathematical Economics
Authors
Series Title
Vector Optimization
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-44723-6
DOI
10.1007/978-3-030-44723-6
Hardcover ISBN
978-3-030-44721-2
Series ISSN
1867-8971
Edition Number
1
Number of Pages
XX, 690
Number of Illustrations
26 b/w illustrations, 67 illustrations in colour
Topics

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