A Long-step barrier method for convex quadratic programming

Abstract

In this paper we propose a long-step logarithmic barrier function method for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps along projected Newton directions are taken until the iterate is in the vicinity of the center associated with the current value of the barrier parameter. We prove that the total number of iterations isO(źnL) orO(nL), depending on how the barrier parameter is updated.