The set of target vectors in a problem of semi-infinite linear programming with a duality gap
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 43-52
Voir la notice de l'article provenant de la source Math-Net.Ru
We propose a geometric method for the analysis of duality relations in a pair of semi-infinite linear programming (SILP) problems. The method is based on the use of the conical hull of the coefficients in the constraint system. A relation between the presence of a duality gap and the nonclosedness of the boundary of the conical hull of points in a multidimensional space is established. The geometric approach is used to construct an opposite pair of dual problems and to explore the duality relation for this pair. We construct a nontrivial example of a SILP problem in which the duality gap occurs for noncollinear target vectors.
Keywords:
semi-infinite linear programming, duality gap, geometric approach, convex nonclosed cone, set of target vectors.
@article{TIMM_2016_22_4_a4,
author = {N. N. Astaf'ev and A. V. Ivanov and S. P. Trofimov},
title = {The set of target vectors in a problem of semi-infinite linear programming with a duality gap},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {43--52},
publisher = {mathdoc},
volume = {22},
number = {4},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a4/}
}
TY - JOUR AU - N. N. Astaf'ev AU - A. V. Ivanov AU - S. P. Trofimov TI - The set of target vectors in a problem of semi-infinite linear programming with a duality gap JO - Trudy Instituta matematiki i mehaniki PY - 2016 SP - 43 EP - 52 VL - 22 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a4/ LA - ru ID - TIMM_2016_22_4_a4 ER -
%0 Journal Article %A N. N. Astaf'ev %A A. V. Ivanov %A S. P. Trofimov %T The set of target vectors in a problem of semi-infinite linear programming with a duality gap %J Trudy Instituta matematiki i mehaniki %D 2016 %P 43-52 %V 22 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a4/ %G ru %F TIMM_2016_22_4_a4
N. N. Astaf'ev; A. V. Ivanov; S. P. Trofimov. The set of target vectors in a problem of semi-infinite linear programming with a duality gap. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 43-52. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a4/