A LONG-STEP BARRIER METHOD FOR CONVEX QUADRATIC-PROGRAMMING

In this paper we propose a long-step logarithmic barrier function meth od for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps alo ng projected Newton directions are taken until the iterate is in the v icinity of the center associated with the current value of the barrier parameter. We prove that the total number of iterations is O(square-r oot nL) or O(nL), depending on how the barrier parameter is updated.