Separation of convex polyhedral sets with column parameters

Milan Hladík

Kybernetika (2008)

  • Volume: 44, Issue: 1, page 113-130
  • ISSN: 0023-5954

Abstract

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Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the description of the given convex polyhedral set. We provide also a lot of examples carried out on PC.

How to cite

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Hladík, Milan. "Separation of convex polyhedral sets with column parameters." Kybernetika 44.1 (2008): 113-130. <http://eudml.org/doc/33916>.

@article{Hladík2008,
abstract = {Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the description of the given convex polyhedral set. We provide also a lot of examples carried out on PC.},
author = {Hladík, Milan},
journal = {Kybernetika},
keywords = {separating hyperplane; parameters; convex polyhedra; solution set; stability set; separating hyperplane; solution set; stability set},
language = {eng},
number = {1},
pages = {113-130},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Separation of convex polyhedral sets with column parameters},
url = {http://eudml.org/doc/33916},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Hladík, Milan
TI - Separation of convex polyhedral sets with column parameters
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 1
SP - 113
EP - 130
AB - Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the description of the given convex polyhedral set. We provide also a lot of examples carried out on PC.
LA - eng
KW - separating hyperplane; parameters; convex polyhedra; solution set; stability set; separating hyperplane; solution set; stability set
UR - http://eudml.org/doc/33916
ER -

References

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  7. Kemp M. C., Kimura Y., Introduction to Mathematical Economics, Springer, New York 1978 Zbl0387.90004MR0506399
  8. Klee V., Separation and support properties of convex sets – a survey, In: Control Theory and the Calculus of Variations (A. V. Balakrishnan, ed.), Academic Press, New York 1969, pp. 235–303 (1969) MR0394357
  9. Nožička F., Guddat J., Hollatz, H., Bank B., Theorie der linearen parametrischen Optimierung, Akademie-Verlag, Berlin 1974 Zbl0284.90053
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  11. Schrijver A., Theory of Linear and Integer Programming, Wiley, Chichester 1998 Zbl0970.90052MR0874114

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