Geodesic
Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case
Kybernetika, Tome 35 (1999) no. 2, p. [177]

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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 problem is strongly regular at the solution.
Classification : 49J52, 90C30, 90C46, 91A65
Keywords: mathematical programs; optimality condition; equilibrium constraints 
@article{KYB_1999__35_2_a2,
     author = {Outrata, Ji\v{r}{\'\i} V.},
     title = {Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case},
     journal = {Kybernetika},
     pages = {[177]},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {1999},
     mrnumber = {1690944},
     zbl = {1274.90484},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999__35_2_a2/}
}
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Outrata, Jiří V. Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case. Kybernetika, Tome 35 (1999) no. 2, p. [177]. http://geodesic.mathdoc.fr/item/KYB_1999__35_2_a2/