A wide neighborhood arc-search interior-point algorithm for convex quadratic programming with box constraints and linear constraints

In this paper, a wide neighborhood arc-search interior-point algorithm for convex quadratic programming with box constrains and linear constraints (BLCQP) is presented. The algorithm searches the optimizers along the ellipses that approximate the entire central path. Assuming a strictly feasible initial point is available, we show that the algorithm has O(n34log(x0-l)Ts0+(w-x0)Tt0ε)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{\frac{3}{4}}\log \frac{{({x^0} - l)^T}{s^0} + {(w - {x^0})^T}{t^0}}{\varepsilon })$$\end{document} iteration complexity bound, which is the best known complexity result for such methods. The numerical results show that our algorithm is effective and promising.