Linear complementarity problems solvable by A single linear program

@article{Mangasarian1976LinearCP,
  title={Linear complementarity problems solvable by A single linear program},
  author={Olvi L. Mangasarian},
  journal={Mathematical Programming},
  year={1976},
  volume={10},
  pages={263-270}
}
  • O. Mangasarian
  • Published 1 December 1976
  • Mathematics
  • Mathematical Programming
It is shown that the linear complementarity problem of finding az inRn such thatMz + q ⩾ 0, z ⩾ 0 andzT(Mz + q) = 0 can be solved by a single linear program in some important special cases including those whenM or its inverse is a Z-matrix, that is a real square matrix with nonpositive off-diagonal elements. As a consequence certain problems in mechanics, certain problems of finding the least element of a polyhedral set and certain quadratic programming problems, can each be solved by a single… 
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  • Mathematics
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  • 1977
TLDR
This note proves a result which improves on a characterization obtained by Mangasarian of the class ofn × n matricesM such that for everyn-vectorq for which the linear complementarity problem (q, M) is feasible, then the problem has a solution.
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  • J. Pang
  • Mathematics
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  • 1979
TLDR
Two least-element characterizations of solutions to the above linear complementarity problem are established and a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented.
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The concept of sufficient matrices of class Z is investigated to obtain additional properties of the solution set and it is shown that if solutions exist, then one must be the least element of the feasible region.
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