Correcting Inconsistency in Linear Inequalities by Minimal Change in the Right Hand Side Vector

Correcting an inconsistent set of linear inequalities by minimal changes in problem data is a well studied problem and up to now several algorithms have been developed to do this task. In this paper, we consider doing the minimal correction using the l2 norm by changing just the right hand vector. A new formulation of the problem is introduced and its relation with the normal solution of the alternative system of the original system is given. Then a generalized Newton algorithm is designed to solve the new formulation. Extensive computational results using this algorithm and conjugate gradient method is reported to demonstrate the advantages and disadvantages of the two algorithms.