WIAS Preprint No. 1146, (2006)

On calculating the normal cone to a finite union of convex polyhedra


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Outrata, Jiří

2010 Mathematics Subject Classification

  • 49J52 90C31


  • limitng normal cone, convex polyhedra, union of polyhedral cones




The paper 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, half spaces, 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.

Appeared in

  • Optimization, 57 (2008) pp. 57--78.

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