Scalarization and Separation by Translation Invariant Functions

Beschreibung

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.

Autor*in

Christiane Tammer

Themen in »Scalarization and Separation by Translation Invariant Functions«

Separation Theorems Vector Optimization Functional Analysis Variational Analysis Decision Making quantitative finance

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“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)
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