Complexity analysis and numerical implementation of a full-Newton step interior-point algorithm for LCCO

In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure for controlling feasible iterations near the central path during the solution process. The favorable polynomial complexity bound for the algorithm with short-step method is obtained, namely O(nlogn𝜖)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(\sqrt {n}\log \frac {n}{\epsilon })$\end{document} which is as good as the linear and convex quadratic optimization analogue. Numerical results are reported to show the efficiency of the algorithm.