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

N. V. Thoai
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N. V. Thoai: University of Trier

Journal of Optimization Theory and Applications, 2000, vol. 107, issue 2, No 8, 354 pages

Abstract: 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.

Keywords: general quadratic programming problem with quadratic constraints; global optimization; branch-and-bound algorithms; duality bounds (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1026437621223

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