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- Title
The Euclidean Steiner tree problem in R<sup>n</sup>: A mathematical programming formulation.
- Authors
Maculan, Nelson; Michelon, Philippe; Xavier, Adilson E.
- Abstract
A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in Rn is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem.
- Subjects
STEINER systems; BLOCK designs; EUCLIDEAN algorithm; ALGORITHMS; NUMBER theory; LAGRANGE equations; DIFFERENTIAL equations
- Publication
Annals of Operations Research, 2000, Vol 96, Issue 1-4, p209
- ISSN
0254-5330
- Publication type
Article
- DOI
10.1023/A:1018903619285