NDLI: A Rigorous Global Filtering Algorithm for Quadratic Constraints*

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A Rigorous Global Filtering Algorithm for Quadratic Constraints*

Content Provider	Springer Nature Link
Author	Lebbah, Yahia Michel, Claude Rueher, Michel
Copyright Year	2005
Abstract	This article introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are often unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraint systems. The drawback of these approaches comes from the fact that the constraints are handled independently. We introduce here a global filtering algorithm that works on a tight linear relaxation of the quadratic constraints. The Simplex algorithm is then used to narrow the domains. Since most implementations of the Simplex work with floating point numbers and thus, are unsafe, we provide a procedure to generate safe linearizations. We also exploit a procedure provided by Neumaier and Shcherbina to get a safe objective value when calling the Simplex algorithm. With these two procedures, we prevent the Simplex algorithm from removing any solution while filtering linear constraint systems. Experimental results on classical benchmarks show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.
Starting Page	47
Ending Page	65
Page Count	19
File Format	PDF
ISSN	13837133
Journal	Constraints
Volume Number	10
Issue Number	1
e-ISSN	15729354
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	global constraints quadratic constraints safe linearizations Computing Methodologies Artificial Intelligence (incl. Robotics) Optimization Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Artificial Intelligence Computational Theory and Mathematics Software

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