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Local convergence in Fermat’s problem. (English) Zbl 0291.90069

90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
Full Text: DOI
[1] L. Cooper, ”Location--allocation problems”,Operations Research 11 (1963) 331--343. · Zbl 0113.14201 · doi:10.1287/opre.11.3.331
[2] L. Cooper, ”Heuristic methods for location--allocation problems”,SIAM Review 6 (1964) 37--52. · Zbl 0956.90014 · doi:10.1137/1006005
[3] L. Cooper, ”Solutions of generalized locational equilibrium problems”,Journal of Regional Science 7 (1967) 1--18. · doi:10.1111/j.1467-9787.1967.tb01419.x
[4] L. Cooper, ”An extension on the generalized Weber problem”,Journal of Regional Science 8 (1968) 181--197. · doi:10.1111/j.1467-9787.1968.tb01323.x
[5] L. Cooper, ”Probabilistic location--allocation problems”, CS/OR Technical Rept. No. 72020, SMU, Dallas, Texas (March 1973).
[6] P. Henrici,Elements of numerical analysis (Wiley, New York, 1966). · Zbl 0158.15303
[7] E. Isaacson and H.B. Keller,Analysis of numerical methods (Wiley, New York, 1966). · Zbl 0168.13101
[8] I. Norman Katz, ”On the convergence of a numerical scheme for solving some locational equilibrium problems”,SIAM Journal of Applied Mathematics 17 (1969) 1224--1231. · Zbl 0187.18001 · doi:10.1137/0117113
[9] I. Norman Katz and L. Cooper, ”An always convergent numerical scheme for a random locational equilibrium problem”,SIAM Journal on Numerical Analysis, to appear. · Zbl 0288.60057
[10] H.W. Kuhn, ”A note on Fermat’s problem”,Mathematical Programming 4 (1973) 98--107. · Zbl 0255.90063 · doi:10.1007/BF01584648
[11] H.W. Kuhn and R.E. Kuenne, ”An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics”,Journal of Regional Science 4 (1962) 21--23. · doi:10.1111/j.1467-9787.1962.tb00902.x
[12] W. Miehle, ”Link--length minimization in networks”,Operations Research 6 (1968) 232--243. · doi:10.1287/opre.6.2.232
[13] J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970). · Zbl 0241.65046
[14] E. Weiszfeld, ”Sur le point pour lequel la somme des distances den points donnés est minimum”,The Tôhoku Mathematical Journal 43 (1937) 355--386. · Zbl 63.0583.01