Yaguang Yang In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search in the sense that they compute a next iterate on a straight line determined by a search direction which approximates the central path. The proposed arc-search interior-point algorithm uses … Read more
In this paper, ellipse is used to approximate the central path of the linear programming. An interior-point algorithm is devised to search the optimizers along the ellipse. The algorithm is proved to be polynomial with the complexity bound $O(n^{\frac{1}{2}}\log(1/\epsilon))$. Numerical test is conducted for problems in Netlib. For most tested Netlib problems, the result shows … Read more
Arc-search is developed for linear programming in \cite{yang09, yang10}. The algorithms search for optimizers along an ellipse that are approximations of the central path. In this paper, the arc-search method is applied to primal-dual path-following interior-point method for convex quadratic programming. A simple algorithm with iteration complexity $O(\sqrt{n}\log(1/\epsilon))$ is devised. Several improvements on the simple … Read more
Arc-search is developed in optimization algorithms. In this paper, simple analytic arcs are used to approximate the central path of the linear programming. The primal-dual path-following interior-point method is then used to search optimizers along the arcs for linear programming. They require fewer iterations to find the optimal solutions in all the tested problems in … Read more