%0 Journal Article
%T A path following interior-point algorithm for semidefinite optimization problem based on new kernel function
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Djeffal, El Amir
%A Djeffal, Lakhdar
%D 2016
%\ 08/01/2016
%V 4
%N 1
%P 35-58
%! A path following interior-point algorithm for semidefinite optimization problem based on new kernel function
%K quadratic programming
%K convex nonlinear programming
%K interior point methods
%R
%X 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 $m>4$.
%U https://jmm.guilan.ac.ir/article_1805_783e5a298d09d5f817ee51668fdce93b.pdf