Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization

We consider higher-order conditions and sensitivity analysis for solutions to equilibrium problems. The conditions for solutions are in terms of quasi-contingent derivatives and involve higher-order complementarity slackness for both the objective and the constraints and under Hölder metric subregul...

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Bibliographic Details
Published in:Journal of global optimization 2022-09, Vol.84 (1), p.205-228
Main Authors: Bao, Nguyen Xuan Duy, Khanh, Phan Quoc, Tung, Nguyen Minh
Format: Article
Language:English
Subjects:
Computer Science
Equilibrium
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Sensitivity analysis
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Summary:We consider higher-order conditions and sensitivity analysis for solutions to equilibrium problems. The conditions for solutions are in terms of quasi-contingent derivatives and involve higher-order complementarity slackness for both the objective and the constraints and under Hölder metric subregularity assumptions. For sensitivity analysis, a formula of this type of derivative of the solution map to a parametric equilibrium problem is established in terms of the same types of derivatives of the data of the problem. Here, the concepts of a quasi-contingent derivative and critical directions are new. We consider open-cone solutions and proper solutions. We also study an important and typical special case: weak solutions of a vector minimization problem with mixed constraints. The results are significantly new and improve recent corresponding results in many aspects.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01129-z