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Vector Optimization Problems and Their Solution Concepts Read chapter Read first chapter

2012 | OriginalPaper | Chapter

11. Vector Variational Principles for Set-Valued Functions

Authors : Christiane Tammer, Constantin Zălinescu

Published in: Recent Developments in Vector Optimization

Publisher: Springer Berlin Heidelberg

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Abstract

Deriving existence results and necessary conditions for approximate solutions of nonlinear optimization problems under week assumptions is an interesting and modern field in optimization theory. It is of interest to show corresponding results for optimization problems without any convexity and compactness assumptions. Ekeland’s variational principle is a very deep assertion about the existence of an exact solution of a slightly perturbed optimization problem in a neighborhood of an approximate solution of the original problem. The importance of Ekeland’s variational principle in nonlinear analysis is well known. Especially, this assertion is very useful for deriving necessary conditions under certain differentiability assumptions. In optimal control Ekeland’s principle can be used in order to prove an ε-maximum principle in the sense of Pontryagin and in approximation theory for deriving ε-Kolmogorov conditions.

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previous chapter Levitin–Polyak Type Well-Posedness in Constrained Optimization
next chapter The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of Set-Valued Optimization Problems Expressed in Terms of Coderivatives
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Metadata
Title
Vector Variational Principles for Set-Valued Functions
Authors
Christiane Tammer
Constantin Zălinescu
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
Book
Recent Developments in Vector Optimization

Print ISBN: 978-3-642-21113-3

Electronic ISBN: 978-3-642-21114-0

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-3-642-21114-0_11

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