Least-Squares Solution of Linear Inequalities

摘要

The paper deals with a system of linear inequalities in a finite dimensional space. When the system is inconsistent, we are interested in vectors that satisfy the system in a least-squares sense. We characterize such least-squares solutions and propose a method to find one of these solutions. It is shown that for any given system of linear inequalities and for any starting point, the method can produce a solution in a finite number of iterations. Computational results are very satisfactory in terms of accuracy and number of iterations. (Author)