A New Kernel Function with an Exponential-Hyperbolic Logarithmic Barrier Term for Linear Optimization

In this paper, we propose an algorithm of an interior point methods to solve a linear problem. The study is based on the new kernel function with exponential-hyperbolic logarithmic barrier term, We prove that the proposed kernel function belongs to the eligible class introduced by Bai et al. in [11].We show that the algorithm has complexity results for large-update methods, respectively. These are the best known complexity results for such methods.