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

Fondamental and Numerical Mathematics Laboratory, Setif 1 Ferhat Abbas University – Ferhat ABBAS, Sétif 19000, Algeria

^* Corresponding author: yasmina.bendaas@univ-setif.dz

Received: 18 March 2024
Accepted: 5 September 2025

Abstract

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, 𝒪(√(n+1)log(n/∊)). 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.