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 sufficient conditio...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1339 |
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| _version_ | 1832558779093221376 |
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| author | Stefan M. Stefanov |
| author_facet | Stefan M. Stefanov |
| author_sort | Stefan M. Stefanov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1b86b37a4acf43b79ac6aca34bb58db3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1b86b37a4acf43b79ac6aca34bb58db32025-02-03T01:31:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200591339136310.1155/IJMMS.2005.1339Convex separable minimization problems with a linear constraint and bounded variablesStefan M. Stefanov0Department of Mathematics, Faculty of Natural Sciences and Mathematics, South-West University “Neofit Rilski”, Blagoevgrad 2700, BulgariaConsider 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.http://dx.doi.org/10.1155/IJMMS.2005.1339 |
| spellingShingle | Stefan M. Stefanov Convex separable minimization problems with a linear constraint and bounded variables International Journal of Mathematics and Mathematical Sciences |
| title | Convex separable minimization problems with a linear
constraint and bounded variables |
| title_full | Convex separable minimization problems with a linear
constraint and bounded variables |
| title_fullStr | Convex separable minimization problems with a linear
constraint and bounded variables |
| title_full_unstemmed | Convex separable minimization problems with a linear
constraint and bounded variables |
| title_short | Convex separable minimization problems with a linear
constraint and bounded variables |
| title_sort | convex separable minimization problems with a linear constraint and bounded variables |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1339 |
| work_keys_str_mv | AT stefanmstefanov convexseparableminimizationproblemswithalinearconstraintandboundedvariables |