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.

DOI

10.3906/mat-1511-108

Keywords

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

First Page

168

Last Page

185

Recommended Citation

PIRHAJI, M, ZANGIABADI, M, & MANSOURI, H (2017). A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization. Turkish Journal of Mathematics 41 (1): 168-185. https://doi.org/10.3906/mat-1511-108