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 appreciate to feasibility and optimality) of the nonconvex quadratically restricted quadratic programming challenge. the belief is to estimate all quadratic phrases through successive linearizations inside of a branching tree utilizing Reformulation-Linearization concepts (RLT). to take action, 4 periods of linearizations (cuts), reckoning on one to 3 parameters, are special. for every type, we express how one can opt for the simplest member with admire to an exact criterion. The cuts brought at any node of the tree are legitimate within the entire tree, and never basically in the subtree rooted at that node. in an effort to increase the computational velocity, the constitution created at any node of the tree is versatile adequate for use at different nodes. Computational effects are said that come with commonplace attempt 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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Additional info for A branch and cut algorithm for nonconvex quadratically constrained quadratic programming
If no neuron can be removed without damaging the network performance, then a single neuron, with all weights set to zero, is introduced in the hidden layer. To evaluate the QIEA in supervised learning problem, a database set for the weekly mean inflow of a Brazilian hydro basin, was used. This base contains eight attributes, with information regarding the mean inflow for the last 3 weeks, the inflow in the previous day, the forecasted accumulated rain for the next 7 days, and the measures collected from fluviometrical stations along the basin during the last 3 days.
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A branch and cut algorithm for nonconvex quadratically constrained quadratic programming by Charles Audet, Pierre Hansen, Brigitte Jaumard