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First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization

First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for... First and second-order approximations are used to establish both necessary and sufficient optimality conditions for local weak efficiency and local firm efficiency in nonsmooth set-constrained vector problems. Even continuity and relaxed convexity assumptions are not imposed. Compactness conditions are also relaxed. Examples are provided to show advantages of the presented results over recent existing ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-008-9049-6
Publisher site
See Article on Publisher Site

Abstract

First and second-order approximations are used to establish both necessary and sufficient optimality conditions for local weak efficiency and local firm efficiency in nonsmooth set-constrained vector problems. Even continuity and relaxed convexity assumptions are not imposed. Compactness conditions are also relaxed. Examples are provided to show advantages of the presented results over recent existing ones.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2008

References