Two unconstrained optimization approaches for the Euclidean κ-centrum location problem

Shaohua Pan, Jein Shan Chen

研究成果: 雜誌貢獻文章同行評審

2 引文 斯高帕斯(Scopus)

摘要

Consider the single-facility Euclidean κ-centrum location problem in Rn. This problem is a generalization of the classical Euclidean 1-median problem and 1-center problem. In this paper, we develop two efficient algorithms that are particularly suitable for problems where n is large by using unconstrained optimization techniques. The first algorithm is based on the neural networks smooth approximation for the plus function and reduces the problem to an unconstrained smooth convex minimization problem. The second algorithm is based on the Fischer-Burmeister merit function for the second-order cone complementarity problem and transforms the KKT system of the second-order cone programming reformulation for the problem into an unconstrained smooth minimization problem. Our computational experiments indicate that both methods are extremely efficient for large problems and the first algorithm is able to solve problems of dimension n up to 10,000 efficiently.

原文英語
頁(從 - 到)1368-1383
頁數16
期刊Applied Mathematics and Computation
189
發行號2
DOIs
出版狀態已發佈 - 2007 六月 15

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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