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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.

An Arc-search Interior Point Method in the N - ∞ Neighborhood for Symmetric Optimization

Kheirfam B.

Fundamenta Informaticae

2016

Vol. 146, nr 3

255--269

In this paper, we propose an arc-search infeasible interior point algorithm for symmetric optimization using the negative infinity neighborhood of the central path. The algorithm searches the optimizers along the ellipses that approximate the entire central path. The convergence of the algorithm is shown for the set of commutative scaling class, which includes some of the most interesting choice of scalings such as xs; sx and the Nesterov-Todd scalings.