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Erschienen in:
Vector Optimization Problems and Their Solution Concepts Kapitel lesen Erstes Kapitel lesen

2012 | OriginalPaper | Buchkapitel

11. Vector Variational Principles for Set-Valued Functions

verfasst von : Christiane Tammer, Constantin Zălinescu

Erschienen in: Recent Developments in Vector Optimization

Verlag: 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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Vorheriges Kapitel Levitin–Polyak Type Well-Posedness in Constrained Optimization
Nächstes Kapitel 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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Metadaten
Titel
Vector Variational Principles for Set-Valued Functions
verfasst von
Christiane Tammer
Constantin Zălinescu
Copyright-Jahr
2012
Verlag
Springer Berlin Heidelberg
Buch
Recent Developments in Vector Optimization

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

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

Copyright-Jahr: 2012

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

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