## AN ESTIMATE OF SOLUTION SET PERTURBATIONS FOR A SYSTEM OF
LINEAR INEQUALITIES

**A.V.LOTOV**

*Published in : Optimization Methods and Software, 1995, 6(1).*

**Abstract**
Hausdorff distance between solution sets of original and perturbed
linear inequalities systems in real partially ordered Banach space is
estimated. The estimation receives a particular simple expression for
finite dimensional case. The concept of condition number for solution
set of a linear inequalities system is suggested. Explicit expressions
of Lipschitz constants are given.

The results of the paper are applied for the evaluation of perturbations of
the feasible set in criterion space in the framework of the
Feasible goals method.

**Keywords**: linear inequalities, solution set, perturbations,
Hausdorff distance, Lipschitz continuity, condition number