On topological types of ordered median functions

An ordered median functions 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. An explicit representation of an ordered median function in max-min f...

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Bibliographic Details
Published in:Optimization 2015-01, Vol.64 (1), p.149-160
Main Authors: Grzybowski, J., Kalcsics, J., Nickel, S., Pallaschke, D., Urbański, R.
Format: Article
Language:English
Subjects:
Ascent
Classification
Cones
convex analysis
Descent
Dimensional analysis
Mathematical analysis
Mathematical functions
max-min representation
Optimization
ordered median functions
Representations
Studies
Topology
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Summary:An ordered median functions 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. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2014.883512