Scalarization and Separation by Translation Invariant Functions

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-UniversityHalle-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.

• Introduction.- Sets and Binary Relations.- Extended Real-Valued Functions.- Translation Invariant Functions.- Minimizers of Translation Invariant Functions.- Vector Optimization in General Spaces.- Multiobjective Optimization.- Variational Analysis.- Special Cases and Functionals Related to φA,k.- Set-Valued Optimization Problems.- Vector Optimization With Variable Domination Structures.- Variational Methods in Topological Vector Spaces.- Algorithms for the Solution of Optimization Problems.- Optimization Under Uncertainty.- Further Applications.

“The reviewer observes that this functional has recently been most useful in the development of scalarization techniques for vector optimization problems. Hence, this book is likely to be very well received by readers.” (Phan Quốc Khánh, Mathematical Reviews, October, 2022)