Note on prime representations of convex polyhedral sets

A. Boneh; R.J. Caron; F.W. Lemire; J.F. McDonald; J. Telgen; T. Vorst

doi:10.1007/BF00940849

Note on prime representations of convex polyhedral sets

A. Boneh
, R.J. Caron
, F.W. Lemire
, J.F. McDonald
, J. Telgen
, T. Vorst

Research output: Contribution to journal › Article › Professional

4 Citations (Scopus)

187 Downloads (Pure)

Abstract

Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.

Original language	English
Pages (from-to)	137-142
Journal	Journal of optimization theory and applications
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/BF00940849
Publication status	Published - 1989

Keywords

Redundancy
Minimal representation
Linear inequalities
Prime representation
Convex polyhedral sets

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10.1007/BF00940849

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title = "Note on prime representations of convex polyhedral sets",

abstract = "Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.",

keywords = "Redundancy, Minimal representation, Linear inequalities, Prime representation, Convex polyhedral sets",

author = "A. Boneh and R.J. Caron and F.W. Lemire and J.F. McDonald and J. Telgen and T. Vorst",

year = "1989",

doi = "10.1007/BF00940849",

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T1 - Note on prime representations of convex polyhedral sets

AU - Boneh, A.

AU - Caron, R.J.

AU - Lemire, F.W.

AU - McDonald, J.F.

AU - Telgen, J.

AU - Vorst, T.

PY - 1989

Y1 - 1989

N2 - Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.

AB - Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.

KW - Redundancy

KW - Minimal representation

KW - Linear inequalities

KW - Prime representation

KW - Convex polyhedral sets

U2 - 10.1007/BF00940849

DO - 10.1007/BF00940849

M3 - Article

SN - 0022-3239

VL - 61

SP - 137

EP - 142

JO - Journal of optimization theory and applications

JF - Journal of optimization theory and applications

IS - 1

ER -

Note on prime representations of convex polyhedral sets

Abstract

Keywords

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