Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric

A vector integer linear programming problem is considered, principle of optimality of which is defined by a partitioning of partial criteria into groups with Pareto preference relation within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semicontinuity of the many-valued mapping that defines the choice function. A formula of quasistability radius is derived for the case of metric $l_p$, $1\leq p\leq\infty$ defined in the space of parameters of the vector criterion. Similar formulae had been obtained before only for combinatorial (boolean) problems with various kinds of parametrization of the principles of optimality in the cases of $l_1$ and $l_{\infty}$ metrics [1–4], and for some game theory problems [5–7].