A primal-dual algorithm for the fermat-weber problem involving mixed gauges

Michelot, Christian; Lefebvre, O.

doi:10.1007/bf02592080

Cited by 35 publications

(22 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical Weiszfeld procedure (2.3), however, may terminate unexpectedly when the singular case happens. Therefore, some alternatives capable of handling the singular case have been contributed, including the primal-dual algorithm [31], the variational inequality approach [25,26], and so on. Nevertheless, the Weiszfeld procedure and its variants are still significantly appreciated because of their attractive performance in practice.…”

Section: The Weiszfeld Proceduresmentioning

confidence: 99%

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

Jiang

Yuan

2011

Comput Optim Appl

View full text Add to dashboard Cite

We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the wellknown location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.

show abstract

Section: The Weiszfeld Proceduresmentioning

confidence: 99%

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

Jiang

Yuan

2011

Comput Optim Appl

View full text Add to dashboard Cite

show abstract

“…The optimal location is (100,100) which is far from other facilities and which is also a nondifferentiable point of the objective function. As that declared in [6], starting from (90, the Weiszfeld's algorithm gives (97.2,97.2)T after 200000 iterations which lasted 342 seconds. Startingfrom the same point, the algorithm of [6] requires 1001 iterations and 1.16 seconds to output (100, 99.99)T. These results were obtained on MATRA 550-CX.…”

Section: Computational Experiencesmentioning

confidence: 99%

A polynomial time algorithm for solving the fermat-weber location problem with mixed norms

Wu¹

1994

Optimization

View full text Add to dashboard Cite

show abstract

“…Convexly constrained Fermat-Weber problems with mixed gauges in any dimension were solved by Plastria (1985) using a cutting plane method, by Michelot and Lefebvre (1987) using a proximal point algorithm which extends to multifacility location problems (Idrissi et al 1989), and by Fliege (2000) using a polynomial interior point method.…”

Section: Gauges and Normsmentioning

confidence: 99%

“…For at least two decades no further work on this topic seems to have been published, and it is only in recent years that interest in asymmetric distance problems has been revived by some location researchers (see Durier and Michelot 1985;Hodgson et al 1987;Michelot and Lefebvre 1987;Idrissi et al 1988Idrissi et al , 1989Drezner and Wesolowsky 1989;Durier 1990;Chen 1991;Plastria 1992b;Buchanan and Wesolowsky 1993;Fliege 1994Fliege , 1997Fliege , 1998Fliege , 2000Plastria 1994;Nickel 1998;Cera and Ortega 2002;Cera et al 2008). All of these contributions concern continuous problems with distances derived from gauges, the asymmetric extensions of norms (see Sect.…”

Section: Introductionmentioning

confidence: 97%

Asymmetric distances, semidirected networks and majority in Fermat–Weber problems

Plastria

2008

Ann Oper Res

View full text Add to dashboard Cite

The Fermat-Weber problem is considered with distance defined by a quasimetric, an asymmetric and possibly nondefinite generalisation of a metric. In such a situation a distinction has to be made between sources and destinations. We show how the classical result of optimality at a destination or a source with majority weight, valid in a metric space, may be generalized to certain quasimetric spaces. The notion of majority has however to be strengthened to supermajority, defined by way of a measure of the asymmetry of the distance, which should be finite. This extended majority theorem applies to most asymmetric distance measures previously studied in literature, since these have finite asymmetry measure.Perhaps the most important application of quasimetrics arises in semidirected networks, which may contain edges of different (possibly zero) length according to direction, or directed edges. Distance in a semidirected network does not necessarily have finite asymmetry measure. But it is shown that an adapted majority result holds nevertheless in this important context, thanks to an extension of the classical node-optimality result to semidirected networks with constraints.Finally the majority theorem is further extended to Fermat-Weber problems with mixed asymmetric distances.

show abstract

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

Cited by 35 publications

References 23 publications

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

A polynomial time algorithm for solving the fermat-weber location problem with mixed norms

Asymmetric distances, semidirected networks and majority in Fermat–Weber problems

Contact Info

Product

Resources

About