Journal of Applied Mathematics
Volume 2004 (2004), Issue 5, Pages 409-431

Polynomial algorithms for projecting a point onto a region defined by a linear constraint and box constraints in n

Stefan M. Stefanov

Department of Mathematics, South-West University “Neofit Rilski,”, Blagoevgrad 2700, Bulgaria

Received 29 September 2003; Revised 6 April 2004

Copyright © 2004 Stefan M. Stefanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the problem of projecting a point onto a region defined by a linear equality or inequality constraint and two-sided bounds on the variables. Such problems are interesting because they arise in various practical problems and as subproblems of gradient-type methods for constrained optimization. Polynomial algorithms are proposed for solving these problems and their convergence is proved. Some examples and results of numerical experiments are presented.