Stability of compatible systems of linear inequalities and linear separability

We consider methods of correction of matrices (or correction of all parameters) of systems of linear constraints (equations and inequalities). We show that the problem of matrix correction of an inconsistent system of linear inequalities with a non-negativity condition is reduced to a linear program. A stability measure of the feasible solution to a linear system is defined as the minimal possible variation of parameters at which this solution does not satisfy the system. The problem of finding the most stable solution to the system is considered. The results are applied to construct an optimal separating hyperplane that is the most stable to variations of the objects. Bibliogr. 15.