We consider a wide class of linear optimization problems with integer variables. In this paper, the lower and upper attainable bounds on the T2-stability radius of the set of extremum solutions are obtained in the situation where solution space and criterion space are endowed with various Hölder’s norms. As corollaries, the T2-stability criterion is formulated, and, furthermore, the T2-stability radius formula is specified for the case where criterion space is endowed with Chebyshev’s norm.