Stability radius of a vector integer linear programming problem: case of a regular norm in the space of criteria

A multicriteria integer linear programming problem of finding a Pareto set is considered. The set of feasible solutions is supposed to be finite. The lower and upper achievable bounds for the radius of stability are obtained using a stability criterion and the Minkowski–Mahler inequality and assuming that the norm is arbitrary in the space of solutions and is monotone in the space of criteria. Bounds for the radius of stability in spaces with the Holder metric are given in corollaries.