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Reformulations in Mathematical Programming: Definitions and Systematics

Published online by Cambridge University Press:  28 January 2009

Leo Liberti
Leo Liberti*
Affiliation:
LIX École Polytechnique, 91128 Palaiseau, France; liberti@lix.polytechnique.fr
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Abstract

A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are widespread in mathematical programming but interestingly they have never been studied under a unified framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations and give several fundamental definitions categorizing useful reformulations in essentially four types (opt-reformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type.

Keywords

Reformulationformulationmodellinearizationmathematical program.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 1 , January 2009 , pp. 55 - 85
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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