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Compact vs. exponential-size LP relaxations

Carr, Robert D.; Lancia, Giuseppe

In this paper, we illustrate by means of examples a technique for formulating compact (i.e. polynomial-size) linear programming relaxations in place of exponential-size models requiring separation algorithms. In the same vein as a celebrated theorem by Grötschel, Lovász and Schrijver, we state the equivalence of compact separation and compact optimization. Among the examples used to illustrate our technique, we introduce a new formulation for the traveling salesman problem, whose relaxation we show as an equivalent to the subtour elimination relaxation. © 2001 Elsevier Science B.V. All rights reserved.