Article contents
The Lazy Travelling Salesman Problem in $\mathbb{R}^2$![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20161010014157944-0656:S1292811907000255:S1292811907000255_eqnU1.gif)
Published online by Cambridge University Press: 20 June 2007
Abstract
We study a parameter (σ)
dependent relaxation of the Travelling Salesman Problem on $\mathbb{R}^2$.
The relaxed problem is reduced to the Travelling Salesman Problem
as $\sigma\rightarrow$
0. For increasing σ it is also an
ordered clustering algorithm for a set of points in $\mathbb{R}^2$
.
A dual formulation is introduced, which reduces the problem to a
convex optimization, provided the minimizer is in the domain of
convexity of the relaxed functional. It is shown that this last
condition is generically satisfied, provided σ is large
enough.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 3 , July 2007 , pp. 538 - 552
- Copyright
- © EDP Sciences, SMAI, 2007
References
- 3
- Cited by