Talk:Weber problem

Formal statement of problem

I want to put in a section immediately after the lede, entitled "Formal statement of problem" and consisting of the following:

The Weber problem is, given points A₁, A₂, ... , A_n in the Euclidean plane, to find point a P so as to

Minimize w₁d(P, A₁) + w₂d(P, A₂) + ... , + w_nd(P, A_n)

where d(.,.) refers to the Euclidean distance. In the Weber problem the given weights w_i are positive and not necessarily equal. In contrast, in the Fermat problem all the weights are not only positive but also equal to each other, while in the attraction–repulsion problem the weights can be unequal and some of them are negative.

Is the above accurate? Duoduoduo (talk) 15:28, 29 July 2013 (UTC)

See below. The Fermat problem differs in another important respect, in that it fixes n = 3. The variant of the problem with equal weights but variable n is not the Fermat problem but the geometric median, also called the Fermat–Weber problem. —David Eppstein (talk) 19:37, 29 July 2013 (UTC)

Merge to Geometric median?

A merge tag has been placed on this article suggesting it be merged to Geometric median, with the edit summary existing and better article on same topic.

Oppose. A reading of this article shows that it's not on the same topic, but rather is on a generalization. "Geometric median" is the solution of a purely mathematical problem, whereas "Weber problem" is a mathematically based problem in operations research and specifically location theory. To merge them would lead to a long, ungainly combined article. Duoduoduo (talk) 18:40, 29 July 2013 (UTC)

Ok, but something is still screwy about this article. It says at the start that it is about sums of distances to n points, but then (by linking to Fermat point when it says what it generalizes, rather than geometric median, and then by the choice of subtopics in the entire rest of the article) it only talks about the three-point version. Is it n (in which case most of the article is far too specific to the case n=3 and it needs to be rewritten to give more general values of n the appropriate weight, per WP:NPOV), or is it only about three points (in which case it is a toy problem rather than a major subarea of location theory)? —David Eppstein (talk) 19:28, 29 July 2013 (UTC)

Well, the article says it's about the case of n points. Obviously the n=3 case is much more tractable than the general case, and it looks to me like the ratio of coverage in the article may well reflect the ratio of results in the literature. The section "Iterative solutions of the Fermat, Weber and attraction-repulsion problem" says When the number of forces is larger than three, it is no longer possible to determine the angles separating the various forces without taking into account the geometry of the location polygon. Geometric and trigonometric methods are then powerless. Iterative optimizing methods are used in such cases. It then gives a couple of references -- I think this section should give a summary of how the cited iterative techniques work (though it seems to me that most Wikipedia articles gloss over the details of iterative technques that they mention). Duoduoduo (talk) 19:45, 29 July 2013 (UTC)

Wrong angle?

In fragment

1- ... the ∠ABE angle of the ABE triangle must be equal to (180° − 120°)= 60°;

must be ∠AEB Jumpow (talk) 18:20, 1 November 2016 (UTC)