A projected Weiszfeld algorithm for the box-constrained Weber location problem (Q425491)
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scientific article; zbMATH DE number 6043909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A projected Weiszfeld algorithm for the box-constrained Weber location problem |
scientific article; zbMATH DE number 6043909 |
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A projected Weiszfeld algorithm for the box-constrained Weber location problem (English)
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8 June 2012
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Weber problem
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box constraints
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fixed-point iteration
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location problems
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Weiszfeld algorithm
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The Weber problem is to find a point in \(\mathbb{R}^n\) that minimizes the weighted sum of Euclidean distances from the \(m\) given points, that is to find NEWLINE\[NEWLINE\text{argmin} f(x)\qquad\text{subject to }x\in\mathbb{R}^n,NEWLINE\]NEWLINE where \(f\) is called the Weber function and it is defined by NEWLINE\[NEWLINEf(x)= \sum^m_{j=1} w_j\| x- a_j\|.NEWLINE\]NEWLINE The authors generalize the Weber problem considering box constraints and propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. Numerical experiments are given.
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