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Duality bound method for the general quadratic programming problem with quadratic constraints. (English) Zbl 0997.90058
Author’s abstract: The purpose of this article is to develop a branch-and-bound algorithm using duality bounds for the general quadratically constrained quadratic programming problem and having the following properties: (i) duality bounds are computed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each nonconvex function is replaced by its convex envelope; (iii) standard convergence properties of branch-and-bound algorithms for nonconvex global optimization problems are guaranteed. Numerical results of preliminary computational experiments for the case of one quadratic constraint are reported.

MSC:
90C20Quadratic programming
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C26Nonconvex programming, global optimization
49M29Methods involving duality in calculus of variations
90C46Optimality conditions, duality
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