Mehrotra predictor-corrector method

Mehrotra Predictor-Corrector Method

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 1989 by Sanjay Mehrotra.

The method is based on the fact that at each iteration of an interior point algorithm it is necessary to compute the Cholesky decomposition (factorization) of a large matrix in order to find the search direction. The factorization step is the most computationally expensive step in the algorithm. Therefore it makes sense to use the same decomposition more than once before recomputing it.

At each iteration of the algorithm, Mehrotra's predictor-corrector method uses the same Cholesky decomposition to find two different directions: a predictor and a corrector.

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. Then, a corrector term is computed: this contains both a centrality term and a second order term.

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. Its corrector step uses the same Cholesky......
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