%A O. L. Mangasarian %T Error Bounds for Inconsistent Linear Inequalities and Programs %D July 1993 %R 1166 %I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN %C MADISON, WI %X For any system of linear inequalities, consistent or not, the norm of the violations of the inequalities by a given point, multiplied by a condition constant that is independent of the point, bounds the distance 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, bounds the distance between a given point and the nonempty set of minimizers of these violations. These results extend error bounds for consistent linear inequalities and linear programs to inconsistent systems.