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On the strong stability of a vector trajectorial problem of the lexicographic optimization. (English. Russian original) Zbl 0966.90066

Discrete Math. Appl. 8, No. 4, 383-389 (1998); translation from Diskretn. Mat. 10, No. 3, 3-9 (1998).
From the text: A combinatorial lexicographic optimization problem is called stable under perturbations of the vector criterion if new lexicographic optima do not appear under small perturbations of parameters of the vector criterion. When we weaken this condition, we arrive at the concept of the strong stability, which means that new lexicographic optimal trajectories can appear but, under any small perturbation, there exists a lexicographic optimal trajectory that preserves the lexicographic optimality. Note that the notion of the strong stability radius was introduced by [V. K. Leont’ev, Probl. Kibern. 35, 169-184 (1979; Zbl 0439.93040)] for the linear single-criterion trajectorial problems.
In this paper we consider a vector trajectorial problem of lexicographic optimization with partial criteria of the types MINSUM, MINMAX, and MINMIN. Sufficient and necessary conditions of the strong stability of this problem are given. Lower attainable bounds for the strong stability radius are found for the case where \(l_\infty\)-norm is defined in the space of the vector criterion parameters.

MSC:

90C27 Combinatorial optimization
90C29 Multi-objective and goal programming
90C31 Sensitivity, stability, parametric optimization

Citations:

Zbl 0439.93040
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