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Constraint propagation on quadratic constraints

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Abstract

This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is taken to ensure that all methods correctly account for rounding errors in the computations. Various tests and examples illustrate the advantage of the presented method.

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Domes, F., Neumaier, A. Constraint propagation on quadratic constraints. Constraints 15, 404–429 (2010). https://doi.org/10.1007/s10601-009-9076-1

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