A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization

Authors: MOHAMMAD PIRHAJI, MARYAM ZANGIABADI, HOSSEIN MANSOURI

Abstract: This paper proposes a second-order Mehrotra-type predictor-corrector feasible interior-point algorithm for semidefinite optimization problems. In each iteration, the algorithm computes the Newton search directions through a new form of combination of the predictor and corrector directions. Using the Ai-Zhang wide neighborhood for linear complementarity problems, it is shown that the complexity bound of the algorithm is $O(\sqrt{n}\log \varepsilon^{-1})$ for the Nesterov-Todd search direction and $O({n}\log \varepsilon^{-1})$ for the Helmberg-Kojima-Monteiro search directions.

Keywords: Semidefinite optimization, Mehrotra-type predictor-corrector algorithm, polynomial complexity

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