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

Nguyen Xuan Duy Bao (), Phan Quoc Khanh () and Nguyen Minh Tung ()
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Nguyen Xuan Duy Bao: University of Science
Phan Quoc Khanh: Ton Duc Thang University
Nguyen Minh Tung: Banking University of Ho Chi Minh City

Journal of Global Optimization, 2022, vol. 84, issue 1, No 9, 205-228

Abstract: Abstract 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.

Keywords: Karush–Kuhn–Tucker conditions; Higher-order complementarity slackness; Hölder metric subregularity; Quasi-contingent derivative; Critical directions; Derivative of solution map; 90C46; 90C31; 90C30; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01129-z

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