Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 89307, 19 pages
doi:10.1155/JAMDS/2006/89307
An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint
Department of Mathematics, South-West University“Neofit Rilski”, Blagoevgrad 2700, Bulgaria
Received 24 May 2005; Accepted 4 October 2005
Copyright © 2006 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 minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.