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Abstract
The article provides formulae for calculating the limiting normal cone introduced by Mordukhovich to a finite union of convex polyhedra. In the first part, special cases of independent interest are considered (almost disjoint cones, halfspaces, orthants). The second part focusses on unions of general polyhedra. Due to the local nature of the normal cone, one may restrict considerations without loss of generality to finite unions of polyhedral cones. First, an explicit formula for the normal cone is provided in the situation of two cones. An algorithmic approach is presented along with a refined, more efficient formula. Afterwards, a general formula for the union of N cones is derived. Finally, an application to the stability analysis of a special type of probabilistic constraints is provided.
†This article is dedicated to Prof. H. Th. Jongen on the occasion of his 60th birthday.
Acknowledgements
The first author gratefully acknowledges support by the DFG Research Center MATHEON Mathematics for key technologies in Berlin. The research of the second author was supported by grant A 103 0405 of the Grant Agency of the Academy of Sciences of the Czech Republic.
Notes
†This article is dedicated to Prof. H. Th. Jongen on the occasion of his 60th birthday.