Article ID: | iaor19951499 |
Country: | Netherlands |
Volume: | 15 |
Issue: | 4 |
Start Page Number: | 187 |
End Page Number: | 192 |
Publication Date: | Apr 1994 |
Journal: | Operations Research Letters |
Authors: | Mangasarian O.L. |
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.