Compact vs. exponential-size LP relaxations

Authors:
Robert D. Carr;Giuseppe Lancia
Affiliations:
Sandia National Labs, Albuquerque, NM, USA;Sandia National Labs, Albuquerque, NM, USA and Dipartimento di Elettronica e Informatica, University of Padua, Padua, Italy
Venue:
Operations Research Letters
Year:
2002

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Abstract

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 Grotschel, Lovasz 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.