| Issue |
ESAIM: COCV
Volume 13, Number 3, July-September 2007
|
|
|---|---|---|
| Page(s) | 538 - 552 | |
| DOI | https://doi.org/10.1051/cocv:2007025 | |
| Published online | 20 June 2007 | |
The Lazy Travelling Salesman Problem in 
1
Weizmann Institute of Science, Rehovot, Israel.
2
Department of Mathematics, Technion, Haifa
32000, Israel; gershonw@math.technion.ac.il
Received:
23
February
2005
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.