An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems

In this article, we propose a root-finding algorithm for solving a quadratic convex separable knapsack problem, which is more straightforward than existing methods and competitive in practice. Besides, we also present an extension of the proposal, which improves its computational time, and then we i...

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Published inJournal of control science and engineering Vol. 2024; pp. 1 - 17
Main Authors Alves, Atécio, Silva, Jônatas O. L., Matioli, Luiz C., Santos, Paulo S. M., Souza, Sissy S.
Format Journal Article
LanguageEnglish
Published New York Hindawi 08.02.2024
John Wiley & Sons, Inc
Wiley
Subjects
Algorithms
Computing time
Knapsack problem
Lagrange multiplier
Methods
Optimization
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Abstract In this article, we propose a root-finding algorithm for solving a quadratic convex separable knapsack problem, which is more straightforward than existing methods and competitive in practice. Besides, we also present an extension of the proposal, which improves its computational time, and then we incorporate the accelerated Anderson’s and Aitken’s fixed-point algorithms to obtain better results. The algorithm only performs function evaluations. We present partial convergence results of the algorithm. Moreover, we illustrate superior computational results in medium and large problems as well as the applicability of the algorithm with real-life applications to show their efficiency.
AbstractList In this article, we propose a root-finding algorithm for solving a quadratic convex separable knapsack problem, which is more straightforward than existing methods and competitive in practice. Besides, we also present an extension of the proposal, which improves its computational time, and then we incorporate the accelerated Anderson’s and Aitken’s fixed-point algorithms to obtain better results. The algorithm only performs function evaluations. We present partial convergence results of the algorithm. Moreover, we illustrate superior computational results in medium and large problems as well as the applicability of the algorithm with real-life applications to show their efficiency.
Author Matioli, Luiz C.
Souza, Sissy S.
Alves, Atécio
Silva, Jônatas O. L.
Santos, Paulo S. M.
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Copyright Copyright © 2024 Atécio Alves et al.
Copyright © 2024 Atécio Alves et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
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SubjectTerms Algorithms
Computing time
Knapsack problem
Lagrange multiplier
Methods
Optimization
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Title An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems
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