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\end{align}</math>
The predictor-corrector method then works by using [[Newton's method]] to obtain the [[affine scaling]] direction. This is achieved by solving the following system of linear equations
<math>J(x,\lambda,s) \begin{bmatrix} \Delta x^\text{aff}\\\Delta\lambda^\text{aff} \\\Delta s^\text{aff}\end{bmatrix} = -F(x,\lambda,s)</math>
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== Step lengths ==
In practical implementations, a version of [[line search]] is performed to obtain the maximal step length that can be taken in the search direction without violating nonnegativity, <math>(x,s) \geq 0</math>.<ref name=":0" />
== Adaptation to Quadratic Programming ==
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