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A class of simplicial restart fixed point algorithms without an extra dimension.(English)Zbl 0441.90112

Math. Program.20, 33-48 (1981).

Page:−5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5Show Scanned Page
scan of Zbl 0441.90112

Cited in3 Reviews

Cited in29 Documents

MSC:

90C99	Mathematical programming
54H25	Fixed-point and coincidence theorems (topological aspects)
65K05	Numerical mathematical programming methods

Keywords:

simplicial restart fixed point algorithms;no extra dimension;approximation of fixed points;convergence conditions;computational experience;triangulation;labelling

Cite Review PDF

Full Text:DOI

References:

[1]	B.C. Eaves, ”Homotopies for computation of fixed points”,Mathematical Programming 3 (1972) 1–22. ·Zbl 0276.55004 ·doi:10.1007/BF01584975
[2]	B.C. Eaves and R. Saigal, ”Homotopies for computation of fixed points on unbounded regions”,Mathematical Programming 3 (1972) 225–237. ·Zbl 0258.65060 ·doi:10.1007/BF01584991
[3]	W. Forster, ”Fixed point algorithms: background and estimates for implementation on array processors”, Faculty of Mathematical Studies, Preprint Series No. 9, University of Southampton, England (1978).
[4]	R. Kellogg, T.-Y. Li and J. Yorke, ”A constructive proof of Brouwer fixed point theorem and computational results”,SIAM Journal on Numerical Mathematics 13 (1976) 473–483. ·Zbl 0355.65037 ·doi:10.1137/0713041
[5]	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 ·doi:10.1007/BF00933874
[6]	G. van der Laan, ”Simplicial fixed point algorithms”, Dissertation, Vrije Universiteit, Amsterdam, The Netherlands (1980). ·Zbl 0464.90046
[7]	G. van der Laan and A.J.J. Talman, ”A restart algorithm for computing fixed points without an extra dimension”,Mathematical Programming 17 (1979) 74–84. ·Zbl 0411.90061 ·doi:10.1007/BF01588226
[8]	G. van der Laan and A.J.J. Talman, ”A restart algorithm without an artificial level for computing fixed points on unbounded regions”, in: H.-O. Peitgen and H.-O. Walther, eds.,Functional differential equations and approximation of fixed points, Lecture Notes in Mathematics 730 (Springer, Berlin, 1979) pp. 247–256. ·Zbl 0447.65019
[9]	G. van der Laan and A.J.J. Talman, ”An improvement of fixed point algorithms by using a good triangulation”,Mathematical Programming 18 (1980) 274–285. ·Zbl 0433.90089 ·doi:10.1007/BF01588323
[10]	G. van der Laan and A.J.J. Talman, ”On the computation of fixed points in the product space of unit simplices and an application to noncooperativeN person games”, Interfaculteit der Actuariële Wetenschappen en Econometrie, Onderzoekverslag 35, Vrije Universiteit, Amsterdam, The Netherlands (1978).
[11]	G. van der Laan and A.J.J. Talman, ”A new subdivision for computing fixed points with a homotopy algorithm”,Mathematical Programming 19 (1980) 78–91. ·Zbl 0438.90104 ·doi:10.1007/BF01581629
[12]	G. van der Laan and A.J.J. Talman, ”Interpretation of the variable dimension fixed point algorithm with an artificial level”, Interfaculteit der Actuariële Wetenschappen en Econometrie, Onderzoekverslag 47, Vrije Universiteit, Amsterdam, The Netherlands (1979). ·Zbl 0447.65019
[13]	G. van der Laan and A.J.J. Talman, ”Convergence and properties of recent variable dimension algorithms”, in: W. Forster, ed.,Numerical solution of highly nonlinear problems (North-Holland, Amsterdam, 1980) pp. 3–36.
[14]	O.H. Merrill, ”Applications and extensions of an algorithm that computes fixed points of certain upper semi-continuous point to set mappings”, Ph.D. Thesis, University of Michigan, Ann Arbor, MI (1972).
[15]	P.M. Reiser, ”A modified integer labelling for complementarity algorithms”, Institut für Operations Research, Universität Zürich, Zürich, Switzerland (1978). ·Zbl 0384.68064
[16]	P.M. Reiser, ”Ein hybrides Verfahren zur Lösung von nichtlinearen Komplementaritätsproblemen und seine Konvergenzeigenschaften”, Dissertation, Eidgenössischen Technischen Hochschule, Zürich, Switzerland (1978). ·Zbl 0398.90099
[17]	R. Saigal, ”On the convergence of algorithms for solving equations that are based on methods of complementary pivoting”,Mathematics of Operations Research 2 (1977) 108–124. ·Zbl 0395.90082 ·doi:10.1287/moor.2.2.108
[18]	H.E. Scarf, ”The approximation of fixed points of a continuous mapping”,SIAM Journal on Applied Mathematics 15 (1967) 1328–1343. ·Zbl 0153.49401 ·doi:10.1137/0115116
[19]	H.E. Scarf,The computation of economic equilibria (Yale University Press, New Haven, CT, 1973). ·Zbl 0311.90009
[20]	A.J.J. Talman, ”Variable dimension fixed point algorithms and triangulations”, Dissertation, Vrije Universiteit, Amsterdam, The Netherlands (1980). ·Zbl 0464.90047
[21]	M.J. Todd,The computation of fixed points and applications (Springer, Berlin, 1976). ·Zbl 0332.54003
[22]	M.J. Todd, ”Improving the convergence of fixed point algorithms”,Mathematical Programming Study 7 (1978) 151–169. ·Zbl 0399.65034
[23]	M.J. Todd, ”Fixed-point algorithms that allow restarting without an extra dimension”, School of Operations Research and Industrial Engineering, Tech. Rept. No. 379, Cornell University Ithaca, NY (1978).
[24]	M.J. Todd, ”Global and local convergence and monotonicity results for a recent variabledimension simplicial algorithm”, in: W. Forster, ed.,Numerical solution of highly nonlinear problems (North-Holland, Amsterdam, 1980) pp. 43–70.
[25]	M.J. Todd and A.H. Wright, ”A variable-dimension simplicial algorithm for antipodal fixed point theorems”, School of Operations Research and Industrial Engineering, Tech. Rept. No. 417, Cornell University, Ithaca, NY (1979). ·Zbl 0456.65024

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.