Local cone approximations in optimization
M. Castellani, M. Pappalardo (2007)
Control and Cybernetics
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Displaying similar documents to “Proto-differentiability of set-valued mappings and its applications in optimization”
Local cone approximations in optimization
Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions
H. Frankowska (1985)
Annales de l'I.H.P. Analyse non linéaire
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Tightly proper efficiency in vector optimization with nearly cone-subconvexlike set-valued maps.
Xu, Y.D., Li, S.J. (2011)
Journal of Inequalities and Applications [electronic only]
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Optimality conditions of vector set-valued optimization problem involving relative interior.
Zhou, Zhiang (2011)
Journal of Inequalities and Applications [electronic only]
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Derived cones to reachable sets of a nonlinear differential inclusion
Aurelian Cernea (2014)
Mathematica Bohemica
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We consider a nonlinear differential inclusion defined by a set-valued map with nonconvex values and we prove that the reachable set of a certain variational inclusion is a derived cone in the sense of Hestenes to the reachable set of the initial differential inclusion. In order to obtain the continuity property in the definition of a derived cone we use a continuous version of Filippov's theorem for solutions of our differential inclusion. As an application, in finite dimensional spaces,...
Optimality conditions of globally efficient solution for vector equilibrium problems with generalized convexity.
Qiu, Qiusheng (2009)
Journal of Inequalities and Applications [electronic only]
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A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints
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...