A lower bound for the complexity of linear optimization from a quantifier-elimination point of view

Grimson, Rafael

doi:10.4230/DagSemProc.07212.3

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A lower bound for the complexity of linear optimization from a quantifier-elimination point of view

Author Rafael Grimson

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 7212
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2007-12-17

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DOI: 10.4230/DagSemProc.07212.3
URN: urn:nbn:de:0030-drops-12837

Subject Classification

Keywords

Quantifier elimination
dense representation
instrinsic
lower bound

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Abstract

We discuss the impact of data structures in quantifier elimination.
We analyze the arithmetic complexity of the feasibility problem in
linear optimization theory as a quantifier-elimination problem. For
the case of polyhedra defined by $2n$ halfspaces in $mathbb{R}^n$ we prove
that, if dense representation is used to code polynomials, any
quantifier-free formula expressing the set of parameters describing
nonempty polyhedra has size $Omega(4^{n})$.

Cite As Get BibTex

Rafael Grimson. A lower bound for the complexity of linear optimization from a quantifier-elimination point of view. In Constraint Databases, Geometric Elimination and Geographic Information Systems. Dagstuhl Seminar Proceedings, Volume 7212, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007) https://doi.org/10.4230/DagSemProc.07212.3

Author Details

Rafael Grimson

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