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On the radii of steadiness, quasi-steadiness, and stability of a vector trajectory problem on lexicographic optimization

We consider a multicriteria problem on lexicographic optimization on a system of subsets of a finite set (a trajectory problem) with a vector criterion function consisting of linear criteria. We investigate different types of steadiness of the lexicographic set under small variations of parameters of the criterion functions. We give formulae for computing the radii of steadiness, quasi-steadiness, and stability in the case of Chebyshev norm in the space of perturbed parameters. The research was supported by the Foundation for Basic Research of the Byelarussian Republic, grants F 23-70 and F 95-70, the International Soros Education Program in Exact Sciences and Foundation DAAD (for the first author).