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

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 separableobjective function over a feasible region defined by linearequality constraints-linear inequality constraint of the form-greater than or equal to- and bounds on the variables. Anecessary and sufficient condition and a sufficient condition areproved for a feasible solution to be an optimal solution to thesetwo problems, respectively. Iterative algorithms of polynomialcomplexity for solving such problems are suggested and convergenceof these algorithms is proved. Some convex functions, importantfor problems under consideration, as well as computational resultsare presented.

Autor: Stefan M. Stefanov



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