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A Wide Neighborhood Second-order Predictor-corrector Interior-point Algorithm for Semidefinite Optimization with Modified Corrector Directions

Kheirfam B., Mohamadi-Sangachin M.

Fundamenta Informaticae

2017

Vol. 153, nr 4

327--346

In this paper, we present a new second-order predictor-corrector interior-point method for semidefinite optimization. The algorithm is based on the wide neighborhood of the central path and modified corrector directions. In the corrector step, we derive the step size and corrector directions which guarantee that new iterate lies in the wide neighborhood. The iteration complexity bound is O(√nlog X0•S0/ɛ) for the Nesterov-Todd direction, which coincides with the best known complexity results for semidefinite optimization. Some numerical results are provided as well.

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.