On max–min representations of ordered median functions

J. Grzybowski; J. Kalcsics; S. Nickel; D. Pallaschke; R. Urbański

doi:10.1080/02331934.2012.750322

On max–min representations of ordered median functions

J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke^*, R. Urbański

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

An ordered median function is a continuous piecewise linear function. It is well known, that in finite dimensional spaces every continuous piecewise linear function admits a max–min representation in terms of its linear functions. We give an explicit representation of an ordered median function in max–min form using a purely combinatorial approach.

Original language	English
Pages (from-to)	339-348
Number of pages	10
Journal	Optimization
Volume	64
Issue number	2
Early online date	23 Jan 2013
DOIs	https://doi.org/10.1080/02331934.2012.750322
Publication status	Published - 1 Feb 2015

Keywords / Materials (for Non-textual outputs)

convex analysis
max–min-representation
ordered median functions

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10.1080/02331934.2012.750322

Cite this

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title = "On max–min representations of ordered median functions",

abstract = "An ordered median function is a continuous piecewise linear function. It is well known, that in finite dimensional spaces every continuous piecewise linear function admits a max–min representation in terms of its linear functions. We give an explicit representation of an ordered median function in max–min form using a purely combinatorial approach.",

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AU - Grzybowski, J.

AU - Kalcsics, J.

AU - Nickel, S.

AU - Pallaschke, D.

AU - Urbański, R.

PY - 2015/2/1

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AB - An ordered median function is a continuous piecewise linear function. It is well known, that in finite dimensional spaces every continuous piecewise linear function admits a max–min representation in terms of its linear functions. We give an explicit representation of an ordered median function in max–min form using a purely combinatorial approach.

KW - convex analysis

KW - max–min-representation

KW - ordered median functions

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U2 - 10.1080/02331934.2012.750322

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M3 - Article

AN - SCOPUS:84921412081

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JO - Optimization

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ER -

On max–min representations of ordered median functions

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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