Milan Hladík. On the separation of parametric convex polyhedral sets with application in MOLP. Appl. Math., 55(4):269–289, 2010.
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We investigate diverse separation properties of two convex polyhedral sets for the case when there are parameters in one row of the constraint matrix. In particular, we deal with the existence, description and stability properties of the separating hyperplanes of such convex polyhedral sets. We present several examples carried out on PC. We are also interested in supporting separation (separating hyperplanes support both the convex polyhedral sets at given faces) and permanent separation (a hyperplane separates the convex polyhedral sets for all feasible parameters). Finally, we show how the developed theory is applicable in multiobjective linear programming.
@article{Hla2010h,
author = "Milan Hlad\'{\i}k",
title = "On the separation of parametric convex polyhedral sets with application in {MOLP}",
journal = "Appl. Math.",
fjournal = "Applications of Mathematics",
volume = "55",
number = "4",
pages = "269-289",
year = "2010",
doi = "10.1007/s10492-010-0021-9",
url = "https://dml.cz/handle/10338.dmlcz/140399",
bib2html_dl_pdf = "http://am.math.cas.cz/am55-4/1.html",
bib2html_dl_html = "https://doi.org/10.1007/s10492-010-0021-9",
abstract = "We investigate diverse separation properties of two convex polyhedral sets for the case when there are parameters in one row of the constraint matrix. In particular, we deal with the existence, description and stability properties of the separating hyperplanes of such convex polyhedral sets. We present several examples carried out on PC. We are also interested in supporting separation (separating hyperplanes support both the convex polyhedral sets at given faces) and permanent separation (a hyperplane separates the convex polyhedral sets for all feasible parameters). Finally, we show how the developed theory is applicable in multiobjective linear programming.",
keywords = "convex polyhedra, parameters, separating hyperplane, supporting hyperplane, solution set, stability set ",
}
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