Interior path following primal-dual algorithms. part II: Convex quadratic programming

We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of O(~/nL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea. The total number of arithmetic operations is shown to be of the order of O(n3L).