On the separation of parametric convex polyhedral sets with application in MOLP
Applications of Mathematics (2010)
- Volume: 55, Issue: 4, page 269-289
- ISSN: 0862-7940
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topHladík, Milan. "On the separation of parametric convex polyhedral sets with application in MOLP." Applications of Mathematics 55.4 (2010): 269-289. <http://eudml.org/doc/37848>.
@article{Hladík2010,
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.},
author = {Hladík, Milan},
journal = {Applications of Mathematics},
keywords = {convex polyhedra; parameters; separating hyperplane; supporting hyperplane; solution set; stability set; convex polyhedra; parameter; separating hyperplane; supporting hyperplane; solution set; stability set},
language = {eng},
number = {4},
pages = {269-289},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the separation of parametric convex polyhedral sets with application in MOLP},
url = {http://eudml.org/doc/37848},
volume = {55},
year = {2010},
}
TY - JOUR
AU - Hladík, Milan
TI - On the separation of parametric convex polyhedral sets with application in MOLP
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 269
EP - 289
AB - 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.
LA - eng
KW - convex polyhedra; parameters; separating hyperplane; supporting hyperplane; solution set; stability set; convex polyhedra; parameter; separating hyperplane; supporting hyperplane; solution set; stability set
UR - http://eudml.org/doc/37848
ER -
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