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 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.