On the Fermat—Weber problem with convex cost functions

Cordellier, F.; Fiorot, J. C.

doi:10.1007/bf01588972

Cited by 19 publications

(6 citation statements)

References 10 publications

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“…If the 2-norm (not 2-norm squared) is used in the objective of (43), the cluster center update subproblem becomes the considerably harder Weber problem [38,100] which locates a center in R n closest in sum of Euclidean distances to a finite set of given points. Choosing the mean of the points assigned to a given cluster as its center minimizes the sum of the 2-norm distances squared between the data points and the cluster center.…”

Section: Stop Whenmentioning

confidence: 99%

Mathematical Programming for Data Mining: Formulations and Challenges

Bradley

Fayyad

Mangasarian

1999

INFORMS Journal on Computing

203

124

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This paper is intended to serve as an overview of a rapidly emerging research and applications area. In addition to providing a general overview, motivating the importance of data mining problems within the area of knowledge discovery in databases, our aim is to list some of the pressing research challenges, and outline opportunities for contributions by the optimization research communities. Towards these goals, we include formulations of the basic categories of data mining methods as optimization problems. We also provide examples of successful mathematical programming approaches to some data mining problems.

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Section: Stop Whenmentioning

confidence: 99%

Mathematical Programming for Data Mining: Formulations and Challenges

Bradley

Fayyad

Mangasarian

1999

INFORMS Journal on Computing

203

124

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“…Since the objective function is convex, it can be demonstrated that an amended version of this algorithm will always leads to an optimal solution (cf. Cordelier and Fiorot [20]).…”

Section: (B) Non-linear Functions Of Access Costmentioning

confidence: 97%

Location of Public Services: A Selective Method‐oriented Survey

Hansen

Peeters

Thisse

1980

Ann Public Coop Econ

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INTRODUCTION NOTATION PART I : CONTINUOUS MODELS I . The Weber problem (a) Euclidean distance (b) Rectilinear distance 2. Extension of the Weber problem (a) Location constraints (b) Non linear functions of access cost (c) The case of an obnoxious facility 3. The Rawls problem (a) Minimax criterion (b) Maximin criterion 4. Bicriterion problem 5. Location-allocation problem 6 . Location of interacting facilities (a) The Weber problem (b) The Rawls problem (*) The authors wish to thank H. BEGUIN and P. HANJOUL for their comments o n a preliminary draft of this paper.

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“…The same paper generalizes the results of Katz (1969) by a slight modification of the iterative scheme. Other solution techniques in the convex case are described by Cordellier and Fiorot (1978).…”

Section: The Gravity Potential Functionmentioning

confidence: 99%