A primal-dual algorithm for a constrained Fermat-Weber problem involving mixed norms

Idrissi, H.; Lefebvre, O.; Michelot, Christian

doi:10.1051/ro/1988220403131

Cited by 17 publications

(5 citation statements)

References 16 publications

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“…Remark 4. Problem (P CA ) can be considered as an extension of a scalar problem studied by Idrissi, Lefebvre and Michelot (1988): (P 0 (º)):…”

Section: A General Formulation Of the Vector-valued Approximation Promentioning

confidence: 99%

“…The aim of this section is to present an algorithm for solving (P CA ) and to extend the results of Idrissi, Lefebvre and Michelot (1988) to a general vectorial control approximation problem.…”

Section: A General Formulation Of the Vector-valued Approximation Promentioning

confidence: 99%

“…These optimality conditions are useful for applying Spingarn's proximal point algorithm (cf. Idrissi, Lefebvre and Michelot, 1988;Spingarn, 1983) for solving problem (P CA ).…”

Section: Surrogate Problems For Linear Vector Optimization Problems Effmentioning

confidence: 99%

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Decision Support for Location Problems in Town Planning

Patz

Spitzner

Tammer

2002

Int Trans Operational Res

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Urban development and town planning need an adequate decision-making process. European cities, in particular, are compact. Urban elements and functions are in a constant state of change. Moreover, the large number of historic buildings and areas means a sensitive and responsible approach must be taken. The aim of this paper is to consider special location problems in town planning. We formulate multi-criteria location problems, derive optimality conditions and present a geometric algorithm and an interactive procedure including a proximal point algorithm for solving multi-criteria location problems. In this paper, we use location theory as a possible method to help determine the location of a children's playground in a newly-built district of Halle, Germany.

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“…Remark 4. Problem (P CA ) can be considered as an extension of a scalar problem studied by Idrissi, Lefebvre and Michelot (1988): (P 0 (º)):…”

Section: A General Formulation Of the Vector-valued Approximation Promentioning

confidence: 99%

Section: A General Formulation Of the Vector-valued Approximation Promentioning

confidence: 99%

See 1 more Smart Citation

Decision Support for Location Problems in Town Planning

Patz

Spitzner

Tammer

2002

Int Trans Operational Res

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“…Now we will construct a proximal point algorithm in order to solve the inclusion (11) using the approach in [1] which is based on the papers [5] and [2].…”

Section: Proximal Point Algorithmmentioning

confidence: 99%

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

Grecksch¹,

Heyde²,

Tammer³

2000

Monte Carlo Methods and Applications

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“…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: 99%

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

Plastria

2008

Ann Oper Res

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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.

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A primal-dual algorithm for a constrained Fermat-Weber problem involving mixed norms

Cited by 17 publications

References 16 publications

Decision Support for Location Problems in Town Planning

Decision Support for Location Problems in Town Planning

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

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

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