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Line 9: The complete search direction is the sum of the predictor direction and the corrector direction. Although there is no theoretical complexity bound on it yet, Mehrotra's predictor-corrector method is widely used in practice.<ref>"In 1989, Mehrotra described a practical algorithm for linear programming that remains the basis of most current software; his work appeared in 1992."<p>{{cite journal\|last=Potra\|first=Florian A.\|coauthors=Stephen J. Wright\|title=Interior-point methods\|journal=Journal of Computational and Applied Mathematics\|volume=124\|year=2000\|pages=~~281-302~~281–302\|doi=10.1016/S0377-0427(00)00433-7}}</ref> Its corrector step uses the same [[Cholesky decomposition]] found during the predictor step in an effective way, and thus it is only marginally more expensive than a standard interior point algorithm. However, the additional overhead per iteration is usually paid off by a reduction in the number of iterations needed to reach an optimal solution. It also appears to converge very fast when close to the optimum. ==References==

Mehrotra predictor–corrector method: Difference between revisions