CONVEX SEPARABLE MINIMIZATION PROBLEMS WITH A LINEAR CONSTRAINT AND BOUNDED VARIABLES

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 sufficien...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2005-07, Vol.2005 (9), p.1339-1363-102
Main Author: Stefanov, Stefan M
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/IJMMS.2005.1339