An efficient parametric kernel function of IPMs for Linear optimization problems

Abstract

In this manuscript, we examine linear optimization problems formulated in the standard format. A novel kernel function is employed to devise a new interior-point algorithm for these problems. The proposed method reduces the number of iterations required for the Netlib test problems. The outcomes are subsequently derived using the self-dual embedding technique. The application of the kernel function facilitates the determination of search directions and the quantification of the distance between the current iteration and the $\mu$-center of the algorithm. Incorporating specific lemmas tailored to this methodology is essential for establishing the optimal limit on iteration complexity. The methodology delineated in the work of K. Roos provides the framework for our investigation. Finally, numerical instances were examined to elucidate the theoretical findings and demonstrate the efficacy of the proposed innovative approach.