#### Sajad Fathi-Hafshejani, Alireza Fakharzadeh J., An interior-point algorithm for semidefinite optimization based on a new parametric kernel function, Vol. 2018 (2018), Article ID 14, pp. 1-24

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DOI: 10.23952/jnfa.2018.14

Received January 6, 2018; Accepted March 26, 2018; Published April 5, 2018

Abstract. In this paper, an interior-point algorithm for Semidefinite Optimization (SDO) problems based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving SDO problems meets $O\left(\sqrt{n}\log{n}\log\frac{n}{\varepsilon}\right)$, iteration complexity bound for large-update methods. Numerical results confirm that our new proposed kernel function is doing well in practice in comparison with some existing kernel functions in the literature.