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Tuy, Hoang

Pivotal methods for computing equilibrium points: unified approach and new restart algorithm. (English) Zbl 0497.90059

Math. Program. 16, 210-227 (1979).
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Cited in 4 Documents

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
54H25 Fixed-point and coincidence theorems (topological aspects)
65H10 Numerical computation of solutions to systems of equations

Keywords:

pivotal methods; computation of equilibrium points; restart algorithm; completely labelled sets; homotopy algorithms

Citations:

Zbl 0128.148; Zbl 0153.494; Zbl 0285.90053
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\textit{H. Tuy}, Math. Program. 16, 210--227 (1979; Zbl 0497.90059)
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References:

[1] K.J. Arrow and F.H. Hahn,General competitive analysis (Oliver and Boyd, Edinburg, 1971). · Zbl 0311.90001
[2] B.C. Eaves, ”Homotopies for computation of fixed points”,Mathematical Programming 3 (1972) 1–22. · Zbl 0276.55004
[3] B.C. Eaves and R. Saigal, ”Homotopies for computation of fixed points on unbounded regions”,Mathematical Programming 3 (1972) 225–237. · Zbl 0258.65060
[4] B.C. Eaves, ”Properly labelled simplices”, in: G.B. Dantzig and B.C. Eaves, eds.,Studies in optimization 10, MAA Studies in Mathematics (1974) pp. 71–93.
[5] B.C. Eaves, ”A short course in solving equations with PL homotopies”,SIAM-AMS Proceedings 9 (1976) 73–143. · Zbl 0343.47048
[6] B.C. Eaves and H.E. Scarf, ”The solutions of systems of piecewise linear equations”,Mathematics of Operations Research 1 (1976) 1–27. · Zbl 0458.65056
[7] F.J. Gould and J.W. Tolle, ”A unified approach to complementarity in optimization”,Discrete Mathematics 7 (1974) 225–272. · Zbl 0289.90035
[8] Hoang Tuy, Nguyen van Thoai and Le dung Muu, ”Un nouvel algorithme de point fixe”,Comptes Rendus de l’Académie des Sciences de Paris 286 (1978) SérieA 783–785. · Zbl 0383.65032
[9] H.W. Kuhn, ”Simplicial approximation of fixed points”,Proceedings of the National Academy of Sciences, USA 61 (1968) 1238–1242. · Zbl 0191.54904
[10] H.W. Kuhn and J.G. MacKinnon, ”Sandwich method for finding fixed points”,Journal of Optimization Theory and Applications 17 (1975) 189–204. · Zbl 0299.65030
[11] C.M. Lemke and J.T. Howson, ”Equilibrium points of bimatrix games”,SIAM Journal on Applied Mathematics 12 (1964) 413–423. · Zbl 0128.14804
[12] O.H. Merrill, ”Applications and extensions of an algorithm that computes fixed points of certain upper semi-continuous point to set mappings”, Thesis, University of Michigan (1972).
[13] H.E. Scarf, ”The approximation of fixed points of a continuous mapping”,SIAM Journal on Applied Mathematics 15 (1967) 1323–1343. · Zbl 0153.49401
[14] H.E. Scarf, with the collaboration of T. Hansen,The computation of economic equilibria (Yale University Press, New Haven, 1973).
[15] M.J. Todd, ”A generalized complementary pivoting algorithm”,Mathematical Programming 6 (1974) 243–263. · Zbl 0285.90053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.