General central path and the largest step general central path following algorithm for linear programming

In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$O (\sqrt n L)$$ \end{document} ineration complexity. It enjoys quadratic convergence if the optimal vertex is nondegenerate.