Mehrotra predictor-corrector method
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Mehrotra's predictor-corrector method in optimization is an implementation of interior point methods. It was proposed in 1991 by Sanjay Mehrotra.
The idea is to first compute an optimizing search direction based on a first order term (predictor). The step size that can be taken in this direction is used to evaluate how much centrality correction is needed. Second, a corrector term is computed: this contains both a centrality term and a second order term.
Therefore, the 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. Its corrector step effectively uses the Cholesky decomposition of the linear system in the predictor step. Thus it has very little overhead. It also appears to converge very fast when close to the optimum.
