Journal of Applied Mathematics
Volume 2004 (2004), Issue 5, Pages 409-431
doi:10.1155/S1110757X04309071
Polynomial algorithms for projecting a point onto a region defined by a linear
constraint and box constraints in ℝn
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.
Abstract
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.