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Cottle, Richard W.

Completely-\(\mathfrak L\) matrices. (English) Zbl 0442.90091

Math. Program. 19, 347-351 (1980).
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Cited in 1 Review
Cited in 22 Documents

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

principal submatrices; linear complementarity problem; strictly semi- monotone matrices; completely-Q matrices
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References:

[1] M. Aganagic and R.W. Cottle, ”OnQ-matrices”, Tech. Rep. SOL 78-9, Department of Operations Research, Stanford University (September 1978).
[2] R.W. Cottle, ”Some recent developments in linear complementarity theory”, in: R.W. Cottle, F. Giannessi and J.L. Lions, eds.,Variational inequalities and complementarity problems: Theory and applications (Wiley, London) to appear. · Zbl 0484.90088
[3] R.W. Cottle and G.B. Dantzig, ”Complementary pivot theory of mathematical programming”,Linear Algebra and Its Applications 1 (1968) 103–125. · Zbl 0155.28403 · doi:10.1016/0024-3795(68)90052-9
[4] R.W. Cottle and R. von Randow, ”OnQ-matrices, centroids, and simplotopes”, Tech. Rep. 79-10, Department of Operations Research, Stanford University (June 1979).
[5] B.C. Eaves, ”The linear complementarity problem”,Management Science 17 (1971) 612–634. · Zbl 0228.15004 · doi:10.1287/mnsc.17.9.612
[6] C.B. Garcia, ”Some classes of matrices in linear complementarity theory”,Mathematical Programming 5 (1973) 299–310. · Zbl 0284.90048 · doi:10.1007/BF01580135
[7] S. Karamardian, ”The complementarity problem”,Mathematical Programming 2 (1972) 107–129. · Zbl 0247.90058 · doi:10.1007/BF01584538
[8] L.M. Kelly and L.T. Watson, ”Q-matrices and spherical geometry”,Linear Algebra and Its Applications 25 (1979) 175–189. · Zbl 0421.90071 · doi:10.1016/0024-3795(79)90017-X
[9] C.E. Lemke, ”Bimatrix equilibrium points and mathematical programming”,Management Science 11 (1965) 681–689. · Zbl 0139.13103 · doi:10.1287/mnsc.11.7.681
[10] 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) pp. 349–384. · Zbl 0227.90043
[11] K.G. Murty, ”On the number of solutions to the complementarity problem and the spanning properties of complementary cones”,Linear Algebra and Its Applications 5 (1972) 65–108. · Zbl 0241.90046 · doi:10.1016/0024-3795(72)90019-5
[12] J.-S. Pang, ”A note on an open problem in linear complementarity”,Mathematical Programming 13 (1977) 360–363. · Zbl 0367.90080 · doi:10.1007/BF01584349
[13] F. Pereira, ”On characterizations of copositive matrices”, Doctoral Dissertation (and Tech. Rept. 72-8), Department of Operations Research, Stanford University (May 1972).
[14] L. Van der Heyden, ”A variable dimension algorithm for the linear complementarity problem,”Mathematical Programming 19 (1980) 328–346 [this issue]. · Zbl 0442.90090 · doi:10.1007/BF01581652
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