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- W2017043023 abstract "Abstract For a nonempty closed set C in a real normed vector space X and an inequality solution set, we present several sufficient conditions for the tangent and contingent cones to their intersection to contain the intersections of the corresponding cones. We not only express the contingent cone to a solution set of inequalities and equalities by the directional (or Frechet) derivatives of the active inequality constraint functions and the Frechet derivatives of the equality constraint functions but also the tangent cone by the Clarke (or lower Dini, or upper Dini) derivatives of the active inequality constraint functions and the directional derivatives of the equality constraint functions. By using a simple property of the function d C − d C c , we characterize these cones by the hypertangent and hypercontingent vectors to the set C . Furthermore, these results allow us to present new constraint qualifications for the Karush–Kuhn–Tucker conditions." @default.
- W2017043023 created "2016-06-24" @default.
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- W2017043023 date "2010-09-01" @default.
- W2017043023 modified "2023-09-30" @default.
- W2017043023 title "Tangent cone and contingent cone to the intersection of two closed sets" @default.
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- W2017043023 doi "https://doi.org/10.1016/j.na.2010.04.042" @default.
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