International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1339-1363
doi:10.1155/IJMMS.2005.1339
Convex separable minimization problems with a linear
constraint and bounded variables
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.
Abstract
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.