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
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