Zhenxiang Wu, Mingwang Zhang, A new primal-dual interior point method for semidefinite optimization based on a hyperbolic kernel function, Vol. 2025 (2025), No. 21, pp. 1-16

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DOI: 10.23952/jnfa.2025.21

Received January 20, 2025; Accepted June 20, 2025; Published July 23, 2025

Abstract. In primal-dual interior-point methods, kernel functions not only determine the search direction and measures the distance of the current iteration point from the $\mu$ -center but also affect the iteration complexity and practical computational efficiency of algorithms. In this paper, we propose a new primal-dual interior-point method for semidefinite optimization based on a hyperbolic kernel function. We derive the iteration bounds for both large-update and small-update methods, which are the best-known complexity results for such methods. We prove the efficiency of the new algorithm via numerical results.

How to Cite this Article:
Z. Wu, M. Zhang, A new primal-dual interior point method for semidefinite optimization based on a hyperbolic kernel function, J. Nonlinear Funct. Anal. 2025 (2025) 21.