Abstract

The paper is devoted to (metric) regularity theory of semi-linear mappings (set-valued mappings whose graphs are finite unions of convex polyhedral sets). The key results relate to mappings associated with certain "complementarity relations" on polyhedral sets that contain as particular case the standard complementarity of dual polyhedral cones. We also show how the well known results of Robinson and Dontchev-Rockafellar on variational inequalities over polyhedral sets follow from the results obtained in the paper.

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Keywords

  • Variational analysis
  • semi-linear mapping
  • variational inequality
  • strong regularity
  • complementarity mapping

Mathematics Subject Classification

49J40, 49J53, 52B11, 90C31

References

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Suggested citation

A. D. Ioffe. “Metric Regularity, Polyhedrality and Complementarity.” Journal of Convex Analysis 25 (2018), No. 2, 571–594. https://doi.org/10.68381/jca25036

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.