Proto-differentiability of set-valued mappings and its applications in optimization
R. T. Rockafellar (1989)
Annales de l'I.H.P. Analyse non linéaire
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R. T. Rockafellar (1989)
Annales de l'I.H.P. Analyse non linéaire
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Xu, Y.D., Li, S.J. (2011)
Journal of Inequalities and Applications [electronic only]
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Qiu, Qiusheng (2009)
Journal of Inequalities and Applications [electronic only]
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Zhou, Zhiang (2011)
Journal of Inequalities and Applications [electronic only]
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Gao, Ying, Yang, Xinmin, Lee, Heung Wing Joseph (2010)
Journal of Inequalities and Applications [electronic only]
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Jiří V. Outrata (1999)
Kybernetika
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The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity...
René Henrion, Jiří Outrata, Thomas Surowiec (2010)
Kybernetika
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In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check...