Error bounds for inconsistent linear inequalities and programs

Authors:
O. L. Mangasarian
Affiliations:
Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI 53706, USA
Venue:
Operations Research Letters
Year:
1994

Citing 13
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Abstract

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.