Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems

A separable convex continuous knapsack problem with a single equality constraint and bounded variables is considered in this paper. Necessary and sufficient condition (characterization) for a feasible solution to be an optimal solution to this problem is stated, and characterization theorem in terms...

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Bibliographic Details
Published inJournal of information & optimization sciences Vol. 42; no. 1; pp. 1 - 16
Main Author Stefanov, Stefan M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.01.2021
Subjects
Convex programming
Knapsack problem
Optimality conditions
Separable programming
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Summary:A separable convex continuous knapsack problem with a single equality constraint and bounded variables is considered in this paper. Necessary and sufficient condition (characterization) for a feasible solution to be an optimal solution to this problem is stated, and characterization theorem in terms of a relaxed problem is formulated and proved. Versions of this problem with a single inequality constraint of the form "less than or equal to" and "greater than or equal to" are also considered, and sufficient conditions for solving these problems are stated and proved, based on the characterization theorem for the original problem. Examples of some convex separable objective functions for the considered problems are presented.
ISSN:0252-2667
2169-0103
DOI:10.1080/02522667.2019.1624048