Article Outline
Keywords
See also
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Balas E, Yu CS (1982) A note on the Weiszfeld–Kuhn algorithm for the general Fermat problem. Managem Sci Res Report 484:1–6
Calamai PH, Conn AR (1980) A stable algorithm for solving the multifacility location problem involving Euclidean distances. SIAM J Sci Statist Comput 1:512–526
Calamai PH, Conn AR (1982) A second-order method for solving the continuous multifacility location problem. In: Numerical Analysis. Proc. 9th Biennial Conf. Dundee, Scotland, pp 1–25
Calamai PH, Conn AR (1987) A projected Newton method for lp norm location problems. Math Program 38:75–109
Chen P-C, Hansen P, Jaumard B, Tuy H (1992) Weber's problem with attraction and repulsion. J Reg Sci
Drezner Z, Wesolowsky GO (1991) The Weber problem on the plane with some negative weights. INFOR 29:87–99
Horst R, Tuy H (1990) Global optimization, deterministic approaches. Springer, Berlin
Kuhn HW (1967) On a pair of dual nonlinear programs. Nonlinear Programming. North-Holland, Amsterdam, pp 38–54
Kuhn HW (1973) A note on Fermat's problem. Math Program 4:94–107
Kuhn HW (1974) Steiner's problem revisited. In: Studies in Optimization. Math. Assoc. America, Washington, DC, pp 52–70
Maranas CD, Floudas CA (1993) A global optimization method for Weber's problem with attraction and repulsion. In: Proc. Large Scale Optimization: State of the Art Conf., Florida Univ., 15-17 Feb. 1993. Kluwer, Dordrecht, pp 259–293
Ostresh LM (1978) On the convergence of a class of iterative methods for solving the Weber location problem. Oper Res 26:597–609
Overton ML (1983) A quadratically convergent method for minimizing a sum of Euclidean norms. Math Program 27:34–63
Plastria F (1992) The effects of majority in Fermat–Weber problems with attraction and repulsion. YUGOR 1
Rosen JB, Xue G-L (1991) Computational comparison of two algorithms for the Euclidean single facility location problem. ORSA J Comput 3:207–212
Tellier L-N (1972) The Weber problem: Solution and interpretation. Geographical Anal 4:215–233
Tellier L-N (1985) Économie patiale: rationalitée économique de l'espace habité. Gaétan Morin, Chicoutimi, Québec
Tellier L-N (1989) The Weber problem: frequency of different solution types and extension to repulsive forces and dynamic processes. J Reg Sci 29:387–405
Tellier L-N, Ceccaldi X (1983) Phenomenes de polarization et de repulsion dans le context du probleme de Weber. Canad Regional Sci Assoc
Tuy H, Al-Khayyal FA (1992) Global optimization of a nonconvex single facility problem by sequential unconstrained convex minimization. J Global Optim 2:61–71
Tuy H, Al-Khayyal FA, Zhou F (1995) A D.C. optimization method for single facility location problems. J Global Optim 2:61–71
Wang CY (1975) On the convergence and rate of convergence of an iterative algorithm for the plant location problem. Qufu Shiyun Xuebao 2:14–25
Weiszfeld E (1937) Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Math J 43:355–386
Witzgall C (1984) Optimal location of a single facility: Mathematical models and concepts. Report Nat Bureau Standards 8388
Xue G-L (1987) A fast convergent algorithm for \( { \text{min} \sum_{\text i = 1}^{\text m} \parallel {\text x} - {\text a}_{\text i} \parallel } \) on a closed convex set. J Qufu Normal Univ 13(3):15–20
Xue G-L (1989) A globally and quadratically convergent algorithm for \( { \text{min} \sum_{\text i = 1}^{\text m} \parallel {\text x} - {\text a}_{\text i} \parallel } \) type plant location problem. Acta Math Applic Sinica 12:65–72
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Maranas, C.D. (2008). Global Optimization in Weber’s Problem with Attraction and Repulsion . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_249
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_249
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering