A Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming

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dc.contributor.authorAudet, Charles
dc.contributor.authorHansen, Pierre
dc.contributor.authorJaumard, Brigitte
dc.contributor.authorSavard, Gilles
dc.date.accessioned2018-06-18T17:47:32Z
dc.date.available2018-06-18T17:47:32Z
dc.date.issued1999-01
dc.date.noteJanuary 1999
dc.description.abstractWe present a branch and cut algorithm that yields in finite time, a globally epsilon-optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizations (cuts), depending on one to three parameters, are detailed. For each class, we show how to select the best member with respect to a precise criterion. The cuts introduced at any node of the tree are valid in the whole tree, and not only within the subtree rooted at that node. In order to enhance the computational speed, the structure created at any node of the tree is flexible enough to be used at other nodes. Computational results are reported. Some problems of the literature are solved, for the first time with a proof of global optimality.
dc.format.extent30 pp
dc.identifier.citationAudet, Charles, Hansen, Pierre, Jaumard, Brigitte, et al.. "A Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming." (1999) <a href="https://hdl.handle.net/1911/101907">https://hdl.handle.net/1911/101907</a>.
dc.identifier.digitalTR99-01
dc.identifier.urihttps://hdl.handle.net/1911/101907
dc.language.isoeng
dc.titleA Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming
dc.typeTechnical report
dc.type.dcmiText
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