Fast algorithm for quadratic knapsack problem

Abstract

The paper considers a quadratic programming problem with a strictly convex separable objective function, a single linear constraint, and two-sided constraints on variables. This problem is commonly called the Convex Knapsack Separable Quadratic Problem, or CKSQP for short. We are interested in an algorithm for solving CKSQP with a linear time complexity. The papers devoted to this topic contain inaccuracies in the description of algorithms and ineffective implementations. In this work, the existing difficulties were overcome.