Abstract
Given a point to set mapf on a simplex with certain conditions, an algorithm for computing fixed points is described. The algorithm operates by following the fixed point as an initially affine function is deformed towardsf.
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References
F.E. Browder, “On continuity of fixed points under deformations of continuous mappings,”Summa Brasilia Mathematica 4, 5 (1960) 183, 191.
G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963).
B.C. Eaves, “An odd theorem,”Proceedings of the American Mathematical Society 26, 3 (1970) 509–513.
B.C. Eaves, “Computing Kakutani fixed points,”SIAM Journal of Applied Mathematics 21, 2 (1971) 236–244.
B.C. Eaves, “On the basic theorem of complementarity,”Mathematical Programming 1 (1971) 68–75.
S. Eilenberg and N. Steenrod,Foundations of algebraic topology (Princeton University Press, Princeton, N.J., 1952).
T. Hansen, “On the approximation of a competitive equilibrium,” dissertation, Yale University, New Haven, 1968.
T. Hansen and H. Scarf, “On the applications of a recent combinatorial algorithm,” (Cowles Foundation Discussion Paper No. 272, April 1969).
H.W. Kuhn, “Some combinatorial lemmas in topology,”IBM J. Research and Development 4 (1960) 518–524.
H.W. Kuhn, “Simplicial approximation of fixed points,”Proceedings of the National Academy of Sciences 61 (1968) 1238–1242.
C.E. Lemke, “Bimatrix equilibrium points and mathematical programming,”Management Science 11, 7 (1965) 681–689.
C.E. Lemke and J.T. Howson, Jr., “Equilibrium points of bimatrix games,”Journal of the Society of Industrial Applied Mathematics 12, 2 (1964) 413–423.
H. Scarf, “The approximation of fixed points of a continuous mapping,”SIAM Journal of Applied Mathematics 15, 5 (1967) 1328–1343.
E.H. Spanier,Algebraic topology (McGraw-Hill, New York, 1966).
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This research was supported in part by Army Research Office Durham Contract DAHC-04-67-C-0028 and in part by NSF Grant GK-5695.
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Eaves, B.C. Homotopies for computation of fixed points. Mathematical Programming 3, 1–22 (1972). https://doi.org/10.1007/BF01584975
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DOI: https://doi.org/10.1007/BF01584975