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A Predictor-corrector Infeasible-interior-point Algorithm for Semidefinite Optimization in a Wide Neighborhood

Kheirfam B.

Fundamenta Informaticae

2017

Vol. 152, nr 1

33--50

In this paper, we propose a predictor-corrector infeasible interior-point algorithm for semidefinite optimization based on the Nesterov-Todd scaling scheme. In each iteration, the algorithm computes the new iterate using a new combination of the predictor and corrector directions. Using the Ai-Zhang's wide neighborhood for linear complementarity problems, and extended to semidefinite optimization by Li and Terlaky, it is shown that the iteration complexity bound of the algorithm is O(n5/4 log ɛ-1 1), where n is the dimension of the problem and ɛ is the required precision.