International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1339-1363

Convex separable minimization problems with a linear constraint and bounded variables

Stefan M. Stefanov

Department of Mathematics, Faculty of Natural Sciences and Mathematics, South-West University “Neofit Rilski”, Blagoevgrad 2700, Bulgaria

Received 30 June 2004; Revised 19 April 2005

Copyright © 2005 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.


Consider the minimization problem with a convex separable objective function over a feasible region defined by linear equality constraint(s)/linear inequality constraint of the form “greater than or equal to” and bounds on the variables. A necessary and sufficient condition and a sufficient condition are proved for a feasible solution to be an optimal solution to these two problems, respectively. Iterative algorithms of polynomial complexity for solving such problems are suggested and convergence of these algorithms is proved. Some convex functions, important for problems under consideration, as well as computational results are presented.