ERROR-BOUNDS FOR INCONSISTENT LINEAR INEQUALITIES AND PROGRAMS

For any system of linear inequalities, consistent or not, the norm of the violations of the inequalities by a given point, multiplied by a c ondition constant that is independent of the point, bounds the distanc e between the point and the nonempty set of points that minimize these violations. Similarly, for a dual pair of possibly infeasible linear programs, the norm of violations of primal-dual feasibility and primal -dual objective equality, when multiplied by a condition constant, bou nds the distance between a given point and the nonempty set of minimiz ers of these violations. These results extend error bounds for consist ent linear inequalities and linear programs to inconsistent systems.