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van der Heyden, Ludo

A variable dimension algorithm for the linear complementarity problem. (English) Zbl 0442.90090

Math. Program. 19, 328-346 (1980).
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Cited in 1 Review
Cited in 20 Documents

MSC:

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

Keywords:

variable dimension algorithm; sequence of subproblems; different dimensions; linear complementarity problem; index-theoretic arguments; nonmonotonic behavior
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References:

[1] R.W. Cottle, ”Completely-Q matrices”,Mathematical Programming 19 (1980) 347–351. · Zbl 0442.90091 · doi:10.1007/BF01581653
[2] 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
[3] G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, NJ, 1963).
[4] B.C. Eaves, ”The linear complementarity problem”,Management Science 17 (1971) 612–634. · Zbl 0228.15004 · doi:10.1287/mnsc.17.9.612
[5] B.C. Eaves and H. Scarf, ”The solution of systems of piecewise linear equations”,Mathematics of Operations Research 1 (1976) 1–31. · Zbl 0458.65056 · doi:10.1287/moor.1.1.1
[6] 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
[7] C.E. Lemke, ”Some pivot schemes for the linear complementarity problem”, in: M.L. Balinski and R.W. Cottle, eds.,Mathematical programming study 7:Complementarity and fixed points problems (North-Holland, Amsterdam, 1978) pp. 15–35. · Zbl 0381.90073
[8] C.E. Lemke and S.J. Grotzinger, ”On generalizing Shapley’s index theory to labelled pseudomanifolds”,Mathematical Programming 10 (1976) 245–262. · Zbl 0345.90058 · doi:10.1007/BF01580670
[9] C.E. Lemke and J.T. Howson, ”Equilibrium points and bimatrix games”,SIAM Journal of Applied Mathematics 12 (1964) 413–423. · Zbl 0128.14804 · doi:10.1137/0112033
[10] H. Scarf, with the collaboration of T. Hansen,The computation of economic equilibria (Yale University Press, New Haven, CT, 1973). · Zbl 0311.90009
[11] L.S. Shapley, ”On balanced games without side payments”, in: T.C. Hu and S.M. Robinson, eds.,Mathematical programming (Academic Press, New York, 1973) pp. 261–290. · Zbl 0267.90100
[12] L.S. Shapley, ”A note on the Lemke–Howson algorithm”, in: M.L. Balinski, ed.,Mathematical programming study 1:Pivoting and extensions (North-Holland, Amsterdam, 1974) pp. 175–189. · Zbl 0366.90133
[13] A. Stickney and L. Watson, ”Digraph models of Bard-type algorithms for the linear complementarity problem”,Mathematics of Operations Research 3 (1978) 322–333. · Zbl 0396.90096 · doi:10.1287/moor.3.4.322
[14] L. Van der Heyden, ”Refinement methods for computing fixed points using primitive sets”, Dissertation, Yale University, New Haven, CT (1979). · Zbl 0498.90070
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