Babahadda, H.; Gadhi, N. Necessary optimality conditions for bilevel optimization problems using convexificators. (English) Zbl 1090.49021 J. Glob. Optim. 34, No. 4, 535-549 (2006). Summary: In this work, we use a notion of convexificator [V. Jeyakumar and D. T. Luc, J. Optimization Theory Appl. 101, No. 3, 599–621 (1999; Zbl 0956.90033)] to establish necessary optimality conditions for bilevel optimization problems. For this end, we introduce an appropriate regularity condition to help us discern the Lagrange-Kuhn-Tucker multipliers. Cited in 35 Documents MSC: 49J52 Nonsmooth analysis 49K99 Optimality conditions 90C25 Convex programming 90C46 Optimality conditions and duality in mathematical programming Keywords:bilevel optimization; convexificator; continuous functions; Lagrange-Kuhn-Tucker multipliers; necessary optimality conditions; regularity condition; Clarke generalized gradient Citations:Zbl 0956.90033 PDFBibTeX XMLCite \textit{H. Babahadda} and \textit{N. Gadhi}, J. Glob. Optim. 34, No. 4, 535--549 (2006; Zbl 1090.49021) Full Text: DOI References: [4] Clarke F.H. (1983). Optimization and Nonsmooth Analysis. Wiley-Interscience. · Zbl 0582.49001 [6] Chen Y., Florian M. (1992), On the geometry structure of Linear Bilevel Programs: A dual approach, technical Report CRT-867, Centre de Recherche sur les transports, Université de Montreal, Montreal, Quebec, Canada. [21] Michel P. and Penot J.-P. (1984), Calcul sous-differentiel pour des fonctions Lipschitziennes et non Lipschitziennes C.R. Acad. Sc. Paris 298. [23] Migdalas A., Pardalos P.M., Varbrand P. (1997), Multilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.