Mehrotra predictor–corrector method: Difference between revisions

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== Derivation ==

The derivation of this section follows the outline by Nocedal and Wright <ref name=":0">{{Cite book|title=Numerical Optimisation|last=Nocedal|first=Jorge|last2=Wright|first2=Stephen J.|publisher=Springer|year=2006|isbn=978-0387-30303-1|___location=United States of America|pages=392-417, 448-496}}</ref>.

=== Predictor step - Affine scaling direction ===

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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 ==

Although the modifications presented by Mehrotra were intended for interior point algorithms for linear programming, the ideas have been extended and successfully applied to [[quadratic programming]] as well <ref name=":0" />.

==References==