The quadratic knapsack problem—a survey

• Published in: Discrete Applied Mathematics Vol. 155; no. 5; pp. 623 - 648
• Main Author: Pisinger, David
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 15.03.2007; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation algorithms; Computer science; control theory; systems; Exact sciences and technology; Mathematical programming; Operational research and scientific management; Operational research. Management science; Quadratic knapsack problem; Semidefinite programming; Theoretical computing; Upper bounds; Valid inequalities; Approximation algorithms; Semidefinite programming; Valid inequalities; Upper bounds; Quadratic knapsack problem; Polytope; Lagrangian; Computer theory; Decomposition method; Semi definite programming; Approximation algorithm; Experimental study; Constrained optimization; Knapsack problem; Relaxation; Upper bound; Objective function; Combinatorics; Quadratic function

The binary quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades. The present paper gives a survey of upper bounds presented in th...