%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.