Authors:
- 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
Part of the book series: Vector Optimization (VECTOROPT)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
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.
Reviews
Authors and Affiliations
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Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany
Christiane Tammer
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Faculty of Engineering and Health, HAWK University of Applied Sciences and Arts Hildesheim/Holzminden/Göttingen, Göttingen, Germany
Petra Weidner
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.
Bibliographic Information
Book Title: Scalarization and Separation by Translation Invariant Functions
Book Subtitle: with Applications in Optimization, Nonlinear Functional Analysis, and Mathematical Economics
Authors: Christiane Tammer, Petra Weidner
Series Title: Vector Optimization
DOI: https://doi.org/10.1007/978-3-030-44723-6
Publisher: Springer Cham
eBook Packages: Business and Management, Business and Management (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-44721-2Published: 29 June 2020
eBook ISBN: 978-3-030-44723-6Published: 28 June 2020
Series ISSN: 1867-8971
Series E-ISSN: 1867-898X
Edition Number: 1
Number of Pages: XX, 690
Number of Illustrations: 10 b/w illustrations, 67 illustrations in colour
Topics: Operations Research/Decision Theory, Optimization, Economic Theory/Quantitative Economics/Mathematical Methods, Calculus of Variations and Optimal Control; Optimization, Continuous Optimization, Quantitative Finance