Geodesic
On two stability types for a multicriteria integer linear programming problem
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 17-30

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a multicriteria integer linear programming problem with a parametrized optimality principle which is implemented by means of partitioning the partial criteria set into non-empty subsets, inside which relations on the set of solutions are based on the Pareto minimum. The introduction of this principle allows us to connect such classical selection functions as Pareto and aggregative-extremal. A quantitative analysis of two types of stability of the problem to perturbations of the parameters of objective functions is given under the assumption that an arbitrary $l_p$-Hölder norm, $1\leq p\leq\infty,$ is given in the solution space, and the Chebyshev norm is given in the criteria space. The formulas for the radii of quasistability and strong quasi-stability are obtained. Criteria of these types of stability are given as corollaries. 
@article{BASM_2020_1_a1,
     author = {Vladimir A. Emelichev and Sergey E. Bukhtoyarov},
     title = {On two stability types for a multicriteria integer linear programming problem},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {17--30},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2020_1_a1/}
}
TY  - JOUR
AU  - Vladimir A. Emelichev
AU  - Sergey E. Bukhtoyarov
TI  - On two stability types for a multicriteria integer linear programming problem
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2020
SP  - 17
EP  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2020_1_a1/
LA  - en
ID  - BASM_2020_1_a1
ER  - 
%0 Journal Article
%A Vladimir A. Emelichev
%A Sergey E. Bukhtoyarov
%T On two stability types for a multicriteria integer linear programming problem
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2020
%P 17-30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2020_1_a1/
%G en
%F BASM_2020_1_a1
Vladimir A. Emelichev; Sergey E. Bukhtoyarov. On two stability types for a multicriteria integer linear programming problem. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 17-30. http://geodesic.mathdoc.fr/item/BASM_2020_1_a1/