Djeffal, E., Djeffal, L. (2016). A path following interior-point algorithm for semidefinite optimization problem based on new kernel function. Journal of Mathematical Modeling, 4(1), 35-58.

El Amir Djeffal; Lakhdar Djeffal. "A path following interior-point algorithm for semidefinite optimization problem based on new kernel function". Journal of Mathematical Modeling, 4, 1, 2016, 35-58.

Djeffal, E., Djeffal, L. (2016). 'A path following interior-point algorithm for semidefinite optimization problem based on new kernel function', Journal of Mathematical Modeling, 4(1), pp. 35-58.

Djeffal, E., Djeffal, L. A path following interior-point algorithm for semidefinite optimization problem based on new kernel function. Journal of Mathematical Modeling, 2016; 4(1): 35-58.

A path following interior-point algorithm for semidefinite optimization problem based on new kernel function

^{}Department of Mathematics, University of Batna 2, Batna, Algeria

Abstract

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is $O(6(m+1)^{\frac{3m+4}{2(m+1)}}\Psi _{0}^{\frac{m+2}{2(m+1)}}\frac{1}{\theta }\log \frac{n\mu ^{0}}{\varepsilon })$, where $m>4$.