Abstract
An algorithm for the linear complementarity problem is developed which uses principal pivots only. The algorithm is shown to be equivalent to Lemke's algorithm. The advantage of the proposed algorithm is that infeasibility tests may be made after each principal pivot. One such test is equivalent to a check whether the matrix satisfies the “plus” condition of copositive plus matrices or the condition of classL 2 of Eaves.
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R.W. Cottle and G.B. Dantzig, “Complementary pivot theory”, in: G.B. Dantzig and A.F. Veinott, Jr., eds.,Mathematics of the decision sciences, Part I (Am. Math. Soc., Providence, R.I., 1968).
G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J. 1963).
B.C. Eaves, “The linear complementarity problem”,Management Science 17 (9) (1971) 612–634.
R.L. Graves, “A principal pivoting simplex algorithm for linear and quadratic programming”,Operations Research 15 (1967) 482–494.
C.E. Lemke, “On complementary pivot theory”, in: G.B. Dantzig and A.F. Veinott, Jr., eds.,Mathematics of the decision sciences, Part I (Am. Math. Soc., Providence, R.I., 1968).
C.E. Lemke, “Recent results on complementarity problems”, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1970).
S.R. McCammon, “On complementary pivoting”, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.S. (1970).
C. van de Panne and A. Whinston, “A parametric simplicial formulation of Houthakker's capacity method,Econometrica 34 (1966) 354–380.
C. van de Panne,Methods for linear and quadratic programming (North-Holland, Amsterdam, 1974).
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Research was partially supported by a grant from the Canadian National Research Council.
The author is indebted to the referees for drawing his attention to the related method developed by McCammon [7], which was not considered in an earlier version.
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van de Panne, C. A complementary variant of Lemke's method for the linear complementary problem. Mathematical Programming 7, 283–310 (1974). https://doi.org/10.1007/BF01585528
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DOI: https://doi.org/10.1007/BF01585528