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JOURNALS // Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy // Archive

Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022 Volume 9, Issue 1, Pages 76–84 (Mi vspua43)

MATHEMATICS

Fast algorithm for quadratic knapsack problem

A. V. Plotkin

St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

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.

Keywords: quadratic programming, knapsack problem, fast algorithms.

UDC: 519.85

MSC: 90C20

Received: 10.06.2021
Revised: 16.06.2021
Accepted: 02.09.2021

DOI: 10.21638/spbu01.2022.108


 English version:
Vestnik St. Petersburg University, Mathematics, 2022, 9:1, 57–63


© Steklov Math. Inst. of RAS, 2024