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Therefore, the search direction is the sum of the predictor direction and the corrector direction.
Althought 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.
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