Robustness in Nonsmooth Nonconvex Optimization Problems

In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex optimization problems with uncertainty data is studied. First various robust constraint qualifications are introduced based on the concept of tangential subdifferential. Further, robust necessary and sufficient opti...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 25; no. 2; pp. 701 - 729
Main Authors: Mashkoorzadeh, F., Movahedian, N., Nobakhtian, S.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.04.2021
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Concavity
Convexity
Econometrics
Fourier Analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Parameter uncertainty
Potential Theory
Robustness
Nonconvex optimization
90C30
49J52
Optimality condition
Nonsmooth optimization
Robustness
90C26
Tangential subdifferential
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary:In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex optimization problems with uncertainty data is studied. First various robust constraint qualifications are introduced based on the concept of tangential subdifferential. Further, robust necessary and sufficient optimality conditions are derived in the absence of the convexity of the uncertain sets and the concavity of the related functions with respect to the uncertain parameters. Finally, the results are applied to obtain the necessary and sufficient optimality conditions for robust weakly efficient solutions in multiobjective programming problems. In addition, several examples are provided to illustrate the advantages of the obtained outcomes.
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-020-00783-5