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.
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Thoai, N.V. Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints. Journal of Optimization Theory and Applications 107, 331–354 (2000). https://doi.org/10.1023/A:1026437621223
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DOI: https://doi.org/10.1023/A:1026437621223