Journal of Optimization Theory and Applications

, Volume 107, Issue 2, pp 331–354

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


  • N. V. Thoai
    • Department of MathematicsUniversity of Trier

DOI: 10.1023/A:1026437621223

Cite this article as:
Thoai, N.V. Journal of Optimization Theory and Applications (2000) 107: 331. doi:10.1023/A:1026437621223


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 constraintsglobal optimizationbranch-and-bound algorithmsduality bounds
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© Plenum Publishing Corporation 2000