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KETABCHI, Saeed; SALAHI, Maziar. Correcting Inconsistency in Linear Inequalities by Minimal Change in the Right Hand Side Vector. In: Computer Science Journal of Moldova. 2009, nr. 2(50), pp. 179-192. ISSN 1561-4042.
|Computer Science Journal of Moldova|
|Numărul 2(50) / 2009 / ISSN 1561-4042|
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.
Linear Inequalities, Convex Optimization, Conjugate Gradient Method, Generalized Newton Method, Barrier Method.