Volume 24, Issue 4
A Projection-Type Method for Solving Various Weber Problems

J. Comp. Math., 24 (2006), pp. 527-538.

Published online: 2006-08

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• Abstract

This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under $l_1,l_2$ and $l_\infty$-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.

• Keywords

Linear variational inequality, Various Weber problems, Projection-type method, Slack technique.

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@Article{JCM-24-527, author = {}, title = {A Projection-Type Method for Solving Various Weber Problems}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {4}, pages = {527--538}, abstract = {

This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under $l_1,l_2$ and $l_\infty$-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8772.html} }
TY - JOUR T1 - A Projection-Type Method for Solving Various Weber Problems JO - Journal of Computational Mathematics VL - 4 SP - 527 EP - 538 PY - 2006 DA - 2006/08 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8772.html KW - Linear variational inequality, Various Weber problems, Projection-type method, Slack technique. AB -

This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under $l_1,l_2$ and $l_\infty$-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.

Jian-lin Jiang & Bo Chen. (1970). A Projection-Type Method for Solving Various Weber Problems. Journal of Computational Mathematics. 24 (4). 527-538. doi:
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