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

Atecio Alves, Jonatas O. L. Silva,Luiz C. Matioli, Paulo S. M. Santos, Sissy S. Souza

Journal of Control Science and Engineering（2024）

Univ Fed Piaui | Univ Fed Maranhao | Univ Fed Parana | Fed Univ Delta Parnaiba

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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.

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Key words

Convex Optimization,Knapsack Problem,Quadratic Programming,Floating-Point Arithmetic,Interior-Point Methods

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