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Optimality and duality results for bilevel programming problem using convexifactors. (English) Zbl 1229.90207
The bilevel programming problem is reformulated as a single mathematical programming problem by using the nonconvex value function of the lower level problem. Sufficient optimality conditions for the bilevel programming problem are obtained, as well as duality results corresponding to Wolfe and Mond-Weier type duals, respectively. To this end the authors consider convexificators and define \(\partial^*\)-convex, \(\partial^*\)-pseudoconvex and \(\partial^*\)-quasiconvex bifunctions based on the work of J. Dutta and S. Chandra [Optimization 53, No. 1, 77–94 (2004; Zbl 1079.90104)] and X. F. Li and J. Z. Zhang [J. Optim. Theory Appl. 131, No. 3, 429–452 (2006; Zbl 1143.90035)].

MSC:
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
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