First and second-order optimality conditions without differentiability in multivalued vector optimization

First and second-order optimality conditions without differentiability in multivalued vector... By developing and using approximations as generalized derivatives of set-valued mappings, we establish both necessary conditions and sufficient conditions of order one and two for various kinds of solutions to a multivalued vector optimization problem with general inequality constraints and high level of nonsmoothness. An emphasis was paid on the important (but still not widely known) so-called envelope-like effect. Our results are more applicable than a number of recent existing ones in many situations as illustrated in detail by examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

First and second-order optimality conditions without differentiability in multivalued vector optimization

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Publisher
Springer Basel
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0330-z
Publisher site
See Article on Publisher Site

Abstract

By developing and using approximations as generalized derivatives of set-valued mappings, we establish both necessary conditions and sufficient conditions of order one and two for various kinds of solutions to a multivalued vector optimization problem with general inequality constraints and high level of nonsmoothness. An emphasis was paid on the important (but still not widely known) so-called envelope-like effect. Our results are more applicable than a number of recent existing ones in many situations as illustrated in detail by examples.

Journal

PositivitySpringer Journals

Published: Mar 8, 2015

References

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