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Proper, reflecting and absorbing facts of complementary cones

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Abstract

A common approach in studying the linear complementarity problem is via the geometry of the complementary cones. In the case of nondegeneracy, the concept of a ‘proper facet’ and a ‘reflecting facet’ have proven useful. This paper extends these concepts to the degenerate case. Under degeneracy, a facet may turn out to be neither proper nor reflecting, but, a third type which we designate as ‘absorbing’. Previous results in this area can be easily extended using these more general definitions.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, 60201, Evanston, IL, USA

    Romesh Saigal

  2. Graduate School of Business Administration, Harvard University, 02163, Boston, MA, USA

    Richard E. Stone

Authors
  1. Romesh Saigal
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  2. Richard E. Stone
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Saigal, R., Stone, R.E. Proper, reflecting and absorbing facts of complementary cones. Mathematical Programming 31, 106–117 (1985). https://doi.org/10.1007/BF02591864

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  • DOI: https://doi.org/10.1007/BF02591864

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