On the solution of multidimensional convex separable continuous knapsack problem with bounded variables

•Multidimensional convex separable continuous knapsack problem is analyzed.•Necessary and sufficient optimality condition is formulated and proved.•Primal-dual analysis of the proposed approach is included.•Examples of convex objective functions for the considered problem are presented. A minimizati...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 247; no. 2; pp. 366 - 369
Main Author Stefanov, Stefan M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2015
Elsevier Sequoia S.A
Subjects
Convex analysis
Convex programming
Knapsack problem
Mathematical functions
Necessary and sufficient optimality conditions
Separable programming
Studies
Convex programming
Necessary and sufficient optimality conditions
Separable programming
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Summary:•Multidimensional convex separable continuous knapsack problem is analyzed.•Necessary and sufficient optimality condition is formulated and proved.•Primal-dual analysis of the proposed approach is included.•Examples of convex objective functions for the considered problem are presented. A minimization problem with a convex separable objective function subject to linear equality constraints and box constraints (bounds on the variables) is considered. Necessary and sufficient optimality condition is proved for a feasible solution to be an optimal solution to this problem. Primal-dual analysis is also included. Examples of some convex separable objective functions for the considered problem are presented.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.06.014