’CONSTRAINTS SORTING METHOD’ NEW APPROACH FOR SOLVING LARGE-SCALE PROBLEMS

Abstract

In this paper, we propose an iterative method for solving very large-scale linear problems called the constraints sorting method (CSM), it consists in sorting the constraints of the initial problem, and iteratively solving a serie of sub-problems of increasing size which will converge to the solution sought, the efficiency of this method depends on the choice of constraints to be introduced, we have chosen to add, at each iteration, a set of constraints most orthogonal to the criterion of the problem to be solved, which gave us very good results. In order to compare (CSM) with the interior point method, we have realized a numerical implementation of our (CSM) approach using the Matlab programming language, and numerical results on execution time showing that our approach is competitive are presented.