A branch and cut algorithm for nonconvex quadratically by Charles Audet, Pierre Hansen, Brigitte Jaumard

By Charles Audet, Pierre Hansen, Brigitte Jaumard

We current a department and minimize set of rules that yields in finite time, a globally ☼-optimal resolution (with recognize to feasibility and optimality) of the nonconvex quadratically limited quadratic programming challenge. the belief is to estimate all quadratic phrases through successive linearizations inside of a branching tree utilizing Reformulation-Linearization ideas (RLT). to take action, 4 periods of linearizations (cuts), reckoning on one to 3 parameters, are designated. for every category, we exhibit the way to pick out the simplest member with appreciate to an actual criterion. The cuts brought at any node of the tree are legitimate within the entire tree, and never in basic terms in the subtree rooted at that node. which will increase the computational velocity, the constitution created at any node of the tree is versatile adequate for use at different nodes. Computational effects are suggested that come with general try difficulties taken from the literature. a few of these difficulties are solved for the 1st time with an evidence of worldwide optimality.

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Nombre impair 0 point extérieur d'intersections. t b+l & pbdow; qui consiste à un ensemble de ~a bonne exécution de l'algorithme implique que l'on sache si on est à l'intérieur ou à l'extérieur de la tache. 10). : de parité. : ,: Mais l'application la majorité des cas, l- arêtes 2- sommets de cet algorithme donne des résultats erronés car il ne tient pas compte des singularités : dans horizontales 3- recouvrements d'arêtes 4- points doubles, etc... 4 - CUNCLUSION En conclusion, les algorithmes de coloriage "e remplissant que des taches con"exes à partir d'un point intérieur (germe) souvent difficiles à déterminer automatiquement, sont avant tout utilisables de manière interactive.

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Existant . Celui d'ACKLAND et "ESTE, , où pour eion des arêtes ils ne conservent qu'un seul point par ligne ce qui entraîoe une légère déformation du contour. : - la quantification engendre souvent plusieurs la même ligne (1) - superposition d'arêtes, très voisines après - certains sommets qui conserve*t le contexte algorithmes . Celui de LUCAS, , qui utilise une adaptation de son algorithme de génération de segments de droite pour engendrer et coder les arêtes en fonction des singularités rencontrées.

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