We study a parameter () dependent relaxation of the Travelling Salesman Problem on . The relaxed problem is reduced to the Travelling Salesman Problem as 0. For increasing 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 is large enough.
Keywords: travelling Salesman problem, Legendre-Fenchel transform
@article{COCV_2007__13_3_538_0,
author = {Polak, Paz and Wolansky, Gershon},
title = {The lazy travelling salesman problem in $\mathbb {R}^2$},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {538--552},
year = {2007},
publisher = {EDP Sciences},
volume = {13},
number = {3},
doi = {10.1051/cocv:2007025},
mrnumber = {2329175},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2007025/}
}
TY - JOUR
AU - Polak, Paz
AU - Wolansky, Gershon
TI - The lazy travelling salesman problem in $\mathbb {R}^2$
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2007
SP - 538
EP - 552
VL - 13
IS - 3
PB - EDP Sciences
UR - https://www.numdam.org/articles/10.1051/cocv:2007025/
DO - 10.1051/cocv:2007025
LA - en
ID - COCV_2007__13_3_538_0
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%A Polak, Paz
%A Wolansky, Gershon
%T The lazy travelling salesman problem in $\mathbb {R}^2$
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2007
%P 538-552
%V 13
%N 3
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/cocv:2007025/
%R 10.1051/cocv:2007025
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%F COCV_2007__13_3_538_0
Polak, Paz; Wolansky, Gershon. The lazy travelling salesman problem in $\mathbb {R}^2$. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 538-552. doi: 10.1051/cocv:2007025
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