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Zbl 1020.90042
Fampa, Marcia; Maculan, Nelson
A new relaxation in conic form for the Euclidean Steiner problem in $\Bbb R^n$. (English)
[J] RAIRO, Oper. Res. 35, No.4, 383-394 (2001). ISSN 0399-0559; ISSN 1290-3868/e

Summary: We present a new mathematical programming formulation for the Euclidean Steiner Tree Problem (ESTP) in $\Bbb R^n$. We relax the integrality constraints 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 $\varepsilon$-optimal solution for this latter problem using interior-point algorithm.

MSC 2000:: *90C27 Combinatorial programming
90C51 Interior-point methods
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C35 Network programming

Keywords: Euclidean Steiner type tree problem; conic form; interior point algorithms

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