​Dr. Imene Touil presented a talk entitled "A Primal-Dual IPM Based on a Bi-Parametric Kernel Function for Linear Programming Problems​​​​​" at the 8th International Conference on Mathematics: An Istanbul Meeting for World Mathematicians ICOM-2024.​

Abstract: Interior-point methods (IPMs) for linear programming (LP) are generally based on the logarithmic barrier functions. In 2001 Peng et al. (J. Comput. Technol., 6, 61-80 (2001)) proposed the first non-logarithmic kernel function (KF). In this talk, we present a primal-dual interior point method for LP problems based on a new class of efficient bi-parametric KFs with trigonometric barrier term. By simple tools, we check that the complexity bounds of the algorithm based on the proposed KF are O(\sqrt n \log n \frac{\log n}{\epsilon}) and O(\sqrt n \frac{\log n}{\epsilon}) iterations for large- and small-update IPMs. These results coincide with the currently best-known iterations complexity.

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