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A Second-order Corrector Infeasible Interior-point Method with One-norm wide Neighborhood for Symmetric Optimization

Kheirfam Behrouz

Fundamenta Informaticae

2020

Vol. 172, nr 4

343--359

In this article, we present a second-order corrector infeasible interior-point method based on one-norm large neighborhood for symmetric optimization. We consider the classical Newton direction as the sum of two other directions associated with the negative and positive parts of the right-hand side of the centrality equation. In addition to equipping them with different step lengths, we add a corrector step that is multiplied by the square of the step length in the expression of the new iterate. The convergence analysis of the algorithm is discussed and it is proved that the new algorithm has the same complexity as small neighborhood infeasible interior-point algorithms for the Nesterov-Todd (NT) direction, and the xs and sx directions.

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.