A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization

In this paper, we present a theoretical and numerical study of a primal-dual path-following interior-point algorithm for solving convex quadratic semidefinite optimization problems (CQSDO). At each iteration, the algorithm uses only feasible full Nesterov-Todd steps for tracing approximately the central-path of CQSDO with the advantage that no line search is computed. Moreover, to ensure its well-definiteness and its locally quadratically convergence to an optimal solution and to enhance its numerical performances, new appropriate defaults are offered. Furthermore, we prove that the algorithm with short-update method has the currently best known polynomial complexity, namely, $ \mathcal{O}(\sqrt{n+1} \log (n / \epsilon)) $. The efficiency of our algorithm is demonstrated through the numerical experiments on some CQSDO problems. Finally, a comparison between the efficiency of our proposed algorithm and existing ones is made.