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A New Relaxation in Conic Form for 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 a new mathematical programming formulation for the Euclidean Steiner Tree Problem (ESTP) in ℜ. We relax the integrality constrains on this formulation and transform the resulting relaxation, which is convex, but not everywhere differentiable, into a standard convex programming problem in conic form. We consider then an efficient computation of an ϵ-optimal solution for this latter problem using interior-point algorithm.

Keywords

Euclidean Steiner tree problemconic forminterior 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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