An O(nL) primal interior point algorithm for convex quadratic programming

Donald Goldfarb, Shucheng Liu

Abstract: We present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach. This approach generates a sequence of problems, each of which is approximately solved by taking a single Newton step. It is shown that the method requires\(O(\sqrt n L)\) iterations and O(n 3.5 L) arithmetic operations. By using modified Newton steps the number of arithmetic operations required by the algorithm can be reduced to O(n 3 L).