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Error bounds and strong upper semicontinuity for monotone affine variational inequalities

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Abstract

Global error bounds for possibly degenerate or nondegenerate monotone affine variational inequality problems are given. The error bounds are on an arbitrary point and are in terms of the distance between the given point and a solution to a convex quadratic program. For the monotone linear complementarity problem the convex program is that of minimizing a quadratic function on the nonnegative orthant. These bounds may form the basis of an iterative quadratic programming procedure for solving affine variational inequality problems. A strong upper semicontinuity result is also obtained which may be useful for finitely terminating any convergent algorithm by periodically solving a linear program.

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Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, 53706, Madison, WI, USA

    M. C. Ferris & O. L. Mangasarian

Authors
  1. M. C. Ferris
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  2. O. L. Mangasarian
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Additional information

This material is based on research supported by Air Force Office of Scientific Research Grant AFOSR-89-0410 and National Science Foundation Grants CCR-9101801 and CCR-9157632.

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Ferris, M.C., Mangasarian, O.L. Error bounds and strong upper semicontinuity for monotone affine variational inequalities. Ann Oper Res 46, 293–305 (1993). https://doi.org/10.1007/BF02023101

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