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A New Relaxation in Conic Formfor the Euclidean Steiner Problem in ℜ

Published online by Cambridge University Press:  15 August 2002

Marcia Fampa  and
Nelson Maculan
Marcia Fampa
Affiliation:
Universidade Federal do Rio de Janeiro, Instituto de Matemática, Departamento de Ciência da Computação, Caixa Postal 68530, Rio de Janeiro, RJ 21945-970, Brazil; fampa@cos.ufrj.br.
Nelson Maculan
Affiliation:
Universidade Federal do Rio de Janeiro, COPPE, Programa de Engenharia de Sistemas e Computação, Caixa Postal 68511, Rio de Janeiro, RJ 21945-970, Brasil; maculan@cos.ufrj.br.
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Abstract

In this paper, we present anew mathematical programming formulation for the Euclidean SteinerTree Problem (ESTP) in ℜ. We relax the integralityconstrains on this formulation and transform the resultingrelaxation, which is convex, but not everywhere differentiable,into a standard convex programming problem in conic form. Weconsider then an efficient computation of an ϵ-optimalsolution for this latter problem using interior-point algorithm.

Keywords

Euclidean Steiner tree problemconicforminterior point algorithms.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 4 , October 2001 , pp. 383 - 394
Copyright
© EDP Sciences, 2001

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