A branch and cut algorithm for nonconvex quadratically constrained quadratic programming | Zendy

Charles Audet | Zendy; Pierre Hansen | Zendy; Brigitte Jaumard | Zendy; Gilles Savard | Zendy

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A branch and cut algorithm for nonconvex quadratically constrained quadratic programming

Author(s) -

Charles Audet,

Pierre Hansen,

Brigitte Jaumard,

Gilles Savard

Publication year - 2000

Publication title -

mathematical programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.358

H-Index - 131

eISSN - 1436-4646

pISSN - 0025-5610

DOI - 10.1007/s101079900106

Subject(s) - quadratic growth , mathematics , tree (set theory) , linearization , mathematical optimization , quadratic programming , quadratic equation , node (physics) , quadratically constrained quadratic program , branch and cut , second order cone programming , algorithm , linear programming , combinatorics , convex optimization , nonlinear system , geometry , physics , structural engineering , quantum mechanics , regular polygon , engineering

We present a branch and cut algorithm that yields in finite time, a globallyffl-optimal solution (with respect to feasibility and optimality) of the nonconvexquadratically constrained quadratic programming problem. The idea is to estimateall quadratic terms by successive linearizations within a branching treeusing Reformulation-Linearization Techniques (RLT). To do so, four classes oflinearizations (cuts), depending on one to three parameters, are detailed. Foreach class, we show how to...

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