A primal-dual interior-point method with full-Newton step for semidefinite optimization

The aim of this paper is to derive a fresh set of search directions for a semidefinite programming problem using Darvay’s technique. The algorithm introduced employs exclusively the full Nesterov–Todd (NT) step in each iteration. We initially establish the local quadratic convergence of the algorithm and subsequently demonstrate that the upper bound for worst-case iterations of the corresponding new algorithm is \(\mathscr {O}\left( q^3 \sqrt{n}\log \frac{n}{\epsilon }\right) ,\) $\mathcal{O}\left(q^3,\sqrt{n},log,\frac{n}{ϵ}\right),$ where \(q\in \mathbb {N}\) $q\in \mathbb{N}$ signifies the small-update method. Notably, this bound aligns with the current state-of-the-art iteration bounds. Finally, some numerical tests are presented on the developed algorithm.