Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems

The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990 ), we obtain the Lagrangian condition for approximate solutions on set-value...

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Bibliographic Details
Published in:Optimization letters Vol. 7; no. 8; pp. 1847 - 1856
Main Authors: Long, X. J., Li, X. B., Zeng, J.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Mordukhovich coderivative
Lagrangian condition
Nonconvex set-valued optimization
Approximate solution
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990 ), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-012-0527-z