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Local convergence in Fermat’s problem. (English) Zbl 0291.90069
MSC:
90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
References:
[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. · 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).
[7]E. Isaacson and H.B. Keller,Analysis of numerical methods (Wiley, New York, 1966).
[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.
[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).
[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.