Convergence study of a second order method on an important class of matrix optimization problems

What is it about?

This paper studies the polynomial complexity and local convergence behavior of an interior point algorithm, a second order algorithm, to solve semi-definite linear complementarity problems using a suitable search direction, Nesterov-Todd search direction, in the algorithm. This is arguably the first time the convergence behavior of the algorithm with this search direction to solve this class of optimization problems is studied.

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Why is it important?

The study in this paper is important since the search direction used in the algorithm is commonly used in implemented interior point softwares, and by understanding the convergence behavior of interior point algorithm using this search direction, the performance of these softwares can be better understood.

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