Li, Jianling; Wang, Peipei; Zeng, Youfang; Jian, Jinbao A long step primal-dual path-following algorithm for convex quadratic semidefinite programming. (Chinese. English summary) Zbl 1474.90319 Acta Math. Appl. Sin. 43, No. 1, 12-32 (2020). Summary: In this paper, based on Nesterov-Todd direction, and by introducing a measure for the central path and a primal-dual logarithmic barrier function, a long step primal-dual path-following algorithm for convex quadratic semidefinite programming is presented. The algorithm ensures that the step size \(l\) is accepted when the iterative point falls into the neighborhood of the central path. An \(\varepsilon\)-optimal solution is obtained after at most \(O (n|\ln \varepsilon|)\) iterations. Some preliminary numerical results are reported. MSC: 90C20 Quadratic programming 90C22 Semidefinite programming 90C25 Convex programming Keywords:convex quadratic semidefinite programming; central path; Nesterov-Todd direction; path-following algorithm; iterative complexity PDFBibTeX XMLCite \textit{J. Li} et al., Acta Math. Appl. Sin. 43, No. 1, 12--32 (2020; Zbl 1474.90319)