**Authors:** V.A.Emelichev, V.G.Pakhilka

### Abstract

A type of the stability of the Pareto, Smale, and Slater sets for a problem of minimizing linear forms over an arbitrary set of substitutions of the symmetric group is investigated. This type of stability assumes that at least one substitution preserves corresponding efficiency for "small" independent perturbations of coefficients of the linear forms. Quantitative bounds of such a type of stability are found.

V.A.Emelichev, V.G.Pakhilka,

Belorussian State University

Ave. F.Skoriny, 4,

Minsk 220050 Belarus

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