# 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} }

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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## 110 Citations

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