Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.Allgower and K.Georg: Simplicial and continuation methods for approximating fixed points and solutions to systems of equations, to appear in SIAM Review, 1979.
H. Brézis: Problèmes unilatéraux, J.Math. pures et appl., 51, pp. 1–168, 1972.
F. Browder: Nonlinear monotone operators and convex sets in Banach spaces, Bull. Amer. Math. Soc., 71, pp. 780–785, 1965.
R.W. Cottle: Nonlinear programs with positively bounded Jacobians, SIAM J. Appl. Math., 14, pp. 147–158, 1966.
J. Dugundji and A. Granas: KKM maps and variational inequalities, Annali della Scuola Normale Superiore di Pisa, Serie IV, Vol. V,4, pp. 679–682, 1978.
B.C. Eaves: Homotopies for computation of fixed points, Mathematical Programming, 3, pp. 1–22, 1972
B.C. Eaves: Computing stationary points, Math. Programming Study, 7, M.L. Balinski and R.W. Cottle, eds., pp. 1–14, North-Holland, Amsterdam, 1978.
B.C. Eaves and R. Saigal: Homotopies for computation of fixed points on unbounded regions, Mathematical Programming, 3, pp. 225–237, 1972
S. Kakutani: A generalization of Brouwer's fixed point theorem, Duke Math. J., 8, pp. 457–459, 1941.
J. Leray and J. Schauder: Topologie et équations fonctionelles, Ann.Sci., Ecole Norm. Sup., 51, 3, pp. 45–78, 1934.
J.L. Lions and G. Stampacchia: Variational inequalities, Comm. Pure Appl. Math., 20, pp.493–519, 1967.
H.J. Lüthi: Komplementaritäts-und Fixpunktalgorithmen in der mathematischen Programmierung, Spieltheorie und Ökonomie, Lecture Notes in Economics and Mathematical Systems, 129, Springer, Heidelberg, 1976.
O.H.Merrill: Applications and extensions of an algorithm that computes fixed points of a certain upper semicontinuous point to set mapping, Ph.D.Thesis, University of Michigan, 1972.
R.T. Rockafellar: Convex analysis, Princeton University Press, Princeton, 1970.
R.Saigal: The fixed point approach to nonlinear programming, to appear in Math. Programming Studies, 1979.
H. Scarf: The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math., 15, pp. 1328–1343, 1967.
M.J. Todd: The computation of fixed points and applications, Lecture Notes in Economics and Mathematical Systems, 124, Springer, New York, 1976.
M.J. Todd: New fixed-point algorithms for economic equilibria and constrained optimization, Technical Report, Cornell University, Ithaca, New York, 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Georg, K. (1979). An application of simplicial algorithms to variational inequalities. In: Peitgen, HO., Walther, HO. (eds) Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064315
Download citation
DOI: https://doi.org/10.1007/BFb0064315
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09518-7
Online ISBN: 978-3-540-35129-0
eBook Packages: Springer Book Archive