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On a class of least-element complementarity problems

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Abstract

The present paper studies the linear complementarity problem of finding vectorsx andy inR n+ such thatc + Dx + y ≧ 0,b − x ≧ 0 andx T (c + Dx + y) = y T (b − x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented. Finally, applications and computational experience with its implementation are discussed.

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Authors and Affiliations

  1. Carnegie-Mellon University, Pittsburgh, PA, USA

    Jong-Shi Pang

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  1. Jong-Shi Pang
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Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.

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Pang, JS. On a class of least-element complementarity problems. Mathematical Programming 16, 111–126 (1979). https://doi.org/10.1007/BF01582097

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  • DOI: https://doi.org/10.1007/BF01582097

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