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Conference Paper

Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45262

Ratschan,  Stefan
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Ratschan, S. (2003). Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities. In Principles and practice on constraint programming - CP 2003: 9th International Conference, CP 2003 (pp. 615-633). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2E22-3
Abstract
This paper contains the first algorithm that can solve disjunctions of constraints of the form $\exists\SVec{y}\STI B \; [ f=0 \;\wedge\; g_1\geq 0\wedge\dots\wedge g_k\geq 0 ]$ in free variables $\SVec{x}$, terminating for all cases when this results in a numerically well-posed problem. Here the only assumption on the terms $f, g_1,\dots, g_n$ is the existence of a pruning function, as given by the usual constraint propagation algorithms or by interval evaluation. The paper discusses the application of an implementation of the resulting algorithm on problems from control engineering, parameter estimation, and computational geometry.