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On two stability types for a multicriteria integer linear programming problem
Authors: Vladimir A.Emelichev, Sergey E.Bukhtoyarov
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Abstract
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 $l_p$-H\"{o}lder 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.Belarusian State University,
av. Nezavisimosti,4, 220030 Minsk
Belarus
E-mail: ,
av. Nezavisimosti,4, 220030 Minsk
Belarus
E-mail: ,
Fulltext
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Contents
- Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product
- On two stability types for a multicriteria integer linear programming problem
- Closure operators in modules and their characterizations
- On the number of topologies on countable skew fields
- New Algorithms for Finding the Limiting and Differential Matrices in Markov Chains
- Solution of the problem of the center for cubic differential systems with three affine invariant straight lines of total algebraic multiplicity four
- On self-adjoint and invertible linear relations generated by integral equations
- Loops with invariant flexibility under the isostrophy
