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

Paz Polak, Gershon Wolansky (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on $ℝ^{2}$ . The relaxed problem is reduced to the Travelling Salesman Problem as $σ \to$ 0. For increasing σ it is also an ordered clustering algorithm for a set of points in $ℝ^{2}$ . 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. ...

Trivial cases for the Kantorovitch problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2000)

RAIRO - Operations Research - Recherche Opérationnelle

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

Let X and Y be two compact spaces endowed with respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on X x Y whose marginals coincide with μ and ν, and such that the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first show that if the cost function c is decomposable, i.e., can be represented as the sum of two continuous functions defined on X and Y, respectively,...

Displaying 1 – 3 of 3

The Lazy Travelling Salesman Problem in ℝ 2

Trivial cases for the Kantorovitch problem

Trivial Cases for the Kantorovitch Problem

Currently displaying 1 – 3 of 3

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