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Journal of Convex Analysis 25 (2018), No. 2, 571--594
Copyright Heldermann Verlag 2018

Metric Regularity, Polyhedrality and Complementarity

Alexander D. Ioffe
Dept. of Mathematics, Technion, Haifa 32000, Israel

The paper is devoted to (metric) regularity theory of semi-linear mappings (set-valued mappings whosegraphs 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.

Keywords: Variational analysis, semi-linear mapping, variational inequality, strong regularity, complementarity mapping.

MSC: 49J40, 49J53, 52B11, 90C31

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