zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A note on the Weber location problem. (English) Zbl 0787.90042
Summary: We collect some interesting and useful results about the Weber problem. We investigate an accelerated Weiszfeld procedure which increases the step size and find a formula for the step size that empirically produces the fastest convergence rate. We also derive an estimate for the optimal cost of the system.
MSC:
90B85Continuous location
References:
[1]R. Chen, Solution of location problems with radial cost function, Comput. Math. Appl. 10(1984)87–94. · Zbl 0524.65046 · doi:10.1016/0898-1221(84)90089-0
[2]R. Chen, Location problems with costs being sums of powers of Euclidean distances, Comput. Oper. Res. 11(1984)285–294. · Zbl 0608.90018 · doi:10.1016/0305-0548(84)90017-0
[3]W. Domschke and A. Drexel,Location and Layout Planning, Lecture Notes in Economics and Mathematical Systems No. 238 (Springer, 1985).
[4]Z. Drezner, The planar two-center and two-median problems, Transp. Sci. 18(1984)351–361. · doi:10.1287/trsc.18.4.351
[5]Z. Drezner and D. Simchi-Levi, Asymptotic behavior of the Weber location problem in the plane, this issue.
[6]R.L. Francis and J.A. White,Facility Layout and Location (Prentice-Hall, Englewood Cliffs, NJ, 1974).
[7]I.N. Katz, On the convergence of a numerica scheme for solving some locational equilibrium problems, SIAM J. Appl. Math. 17(1969)1224–1231. · Zbl 0187.18001 · doi:10.1137/0117113
[8]I.N. Katz, Local convergence in Fermat’s problem, Math. Progr. 6(1974)89–104. · Zbl 0291.90069 · doi:10.1007/BF01580224
[9]H.W. Kuhn, On a pair of dual non-linear problems, in:Non-Linear Programming, ed. J. Abadie (Wiley, New York, 1967).
[10]R.F. Love and P.D. Dowling, A generalized bounding method for multifacility location models, Oper. Res. 37(1989)653–657. · Zbl 0675.90024 · doi:10.1287/opre.37.4.653
[11]R.F. Love, J.G. Morris and G.O. Wesolowsky,Facilities Location Models and Methods (North-Holland, New York, 1988).
[12]J.G. Morris, Convergences of the Weiszfeld algorithm for the Weber problem using generalized ”distance” functions, Oper. Res. 29(1981)37–48. · Zbl 0452.90023 · doi:10.1287/opre.29.1.37
[13]L.M. Ostresh, Jr., On the convergence of a class of iterative methods for solving the Weber location problem, Oper. Res. 26(1978)597–609. · Zbl 0396.90073 · doi:10.1287/opre.26.4.597
[14]E. Weiszfeld, Sur le point pour lequel la somme des distances den points donnés est minimum, Tohoku Math. J. 43(1937)355–386.