Best network flow bounds for the quadratic knapsack problem. (English) Zbl 0678.90061

Combinatorial optimization, Proc. 3rd Sess., Como/Italy 1986, Lect. Notes Math. 1403, 225-235 (1989).
Summary: [For the entire collection see Zbl 0676.00023.]
A Lagrangean relaxation of the quadratic knapsack problem is studied. It is shown, among other properties, that the best value of the Lagrangean multiplier, and hence the best bound for the original problem, can be determined in at most n-1 applications of a maximum flow algorithm to a network with \(n+2\) vertices and \(n+m\) arcs, where n and m denote the numbers of variables and of quadratic terms. A branch-and-bound algorithm using this result is presented and computational experience is reported on.


90C09 Boolean programming
90B10 Deterministic network models in operations research
65K05 Numerical mathematical programming methods
90C35 Programming involving graphs or networks
90C20 Quadratic programming
68Q25 Analysis of algorithms and problem complexity


Zbl 0676.00023