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An O(n) algorithm for quadratic knapsack problems. (English) Zbl 0544.90086
Summary: An algorithm is presented which solves bounded quadratic optimization problems with n variables and one linear constraint in at most O(n) steps. The algorithm is based on a parametric approach combined with well-known ideas for constructing efficient algorithms. It improves an O(n log n) algorithm which has been developed for a more restricted case of the problem.

MSC:
90C20 Quadratic programming
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C25 Convex programming
68Q25 Analysis of algorithms and problem complexity
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References:
[1] Aho, A.; Hopcroft, J.; Ullman, J., The design and analysis of computer algorithms, (1974), Addison-Wesley Reading, MA
[2] Helgason, R.; Kennington, J.; Lall, H., A polynomially bounded algorithm for a single constrainted quadratic program, Mathematical programming, 18, 338-343, (1980) · Zbl 0452.90054
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