Journal of Optimization Theory and Applications

, Volume 107, Issue 2, pp 331-354

First online:

Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints

  • N. V. ThoaiAffiliated withDepartment of Mathematics, University of Trier

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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.

general quadratic programming problem with quadratic constraints global optimization branch-and-bound algorithms duality bounds