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The Lazy Travelling Salesman Problem in $\mathbb{R}^2$

Published online by Cambridge University Press:  20 June 2007

Paz Polak  and
Gershon Wolansky
Paz Polak
Affiliation:
Weizmann Institute of Science, Rehovot, Israel.
Gershon Wolansky
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel; gershonw@math.technion.ac.il
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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 Problemas $\sigma\rightarrow$ 0. For increasing σ it is also anordered clustering algorithm for a set of points in $\mathbb{R}^2$ .A dual formulation is introduced, which reduces the problem to aconvex optimization, provided the minimizer is in the domain ofconvexity of the relaxed functional. It is shown that this lastcondition is generically satisfied, provided σ is largeenough.

Keywords

Travelling Salesman ProblemLegendre-Fenchel transform
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

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