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== Optimization problem ==
{{main|Support vector machine#Formalization}}
Consider a [[binary classification]] problem with a dataset (''x''<sub>1</sub>, ''y''<sub>1</sub>), ..., (''x''<sub>''n''</sub>, ''y''<sub>''n''</sub>), where ''x''<sub>''i''</sub> is an input vector and {{nobr|''y''<sub>''i''</sub> ∈ {-1, +1} }} is a binary label corresponding to it. A soft-margin [[support vector machine]] is trained by solving an optimization problem whose [[
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