Volume 13, Number 3, July-September 2007
|Page(s)||538 - 552|
|Published online||20 June 2007|
The Lazy Travelling Salesman Problem in
Weizmann Institute of Science, Rehovot, Israel.
2 Department of Mathematics, Technion, Haifa 32000, Israel; firstname.lastname@example.org
Revised: 31 January 2006
We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on . The relaxed problem is reduced to the Travelling Salesman Problem as 0. For increasing σ it is also an ordered clustering algorithm for a set of points in . 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.
Mathematics Subject Classification: 49K30 / 49K35 / 65K10
Key words: Travelling Salesman Problem / Legendre-Fenchel transform
© EDP Sciences, SMAI, 2007
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