University of GuilanJournal of Mathematical Modeling2345-394X12220240701Complexity analysis of primal-dual interior-point methods for convex quadratic programming based on a new twice parameterized kernel function247265754310.22124/jmm.2024.25394.2257ENYoussraBouhenacheLaboratory of Pure and Applied Mathematics, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria0000-0002-1934-9873WidedChikoucheLaboratory of Pure and Applied Mathematics, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria0000-0002-4856-1507ImeneTouilLaboratory of Pure and Applied Mathematics, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria0000-0003-2503-1033SajadFathi-HafshejaniShiraz University of Technology, Fars 71557-13876, Shiraz, Iran0000-0002-9907-0695Journal Article20230827In this paper, we present primal-dual interior-point methods (IPMs) for convex quadratic programming (CQP) based on a new twice parameterized kernel function (KF) with a hyperbolic barrier term. To our knowledge, this is the first KF with a twice parameterized hyperbolic barrier term. By using some conditions and simple analysis, we derive the currently best-known iteration bounds for large- and small-update methods, namely, $\textbf{O}\big(\sqrt{n}\log n\log\frac{n}{\epsilon}\big)$ and $\textbf{O}\big(\sqrt{n}\log\frac{n}{\epsilon}\big)$, respectively, with special choices of the parameters. Finally, some numerical results regarding the practical performance of the new proposed KF are reported.https://jmm.guilan.ac.ir/article_7543_a28e724eaad53c6848c2cc9b36b74e72.pdf