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Reduction of affine variational inequalities

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  • Stephen M. Robinson

    (University of Wisconsin–Madison)

Abstract

We consider an affine variational inequality posed over a polyhedral convex set in n-dimensional Euclidean space. It is often the case that this underlying set has dimension less than n, or has a nontrivial lineality space, or both. We show that when the variational inequality satisfies a well known regularity condition, we can reduce the problem to the solution of an affine variational inequality in a space of smaller dimension, followed by some simple linear-algebraic calculations. The smaller problem inherits the regularity condition from the original one, and therefore it has a unique solution. The dimension of the space in which the smaller problem is posed equals the rank of the original set: that is, its dimension less the dimension of the lineality space.

Suggested Citation

  • Stephen M. Robinson, 2016. "Reduction of affine variational inequalities," Computational Optimization and Applications, Springer, vol. 65(2), pages 493-509, November.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:2:d:10.1007_s10589-015-9796-7
    DOI: 10.1007/s10589-015-9796-7
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    2. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
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