On the long step path following method for semide nite pro gramming

It has been shown in various recent research reports that the analysis of short step primal dual path following algorithms for linear programming can be nicely generalized to semide nite programming How ever the analysis of long step path following algorithms for semide nite programming appeared to be less straightforward For such an algorithm Monteiro obtained an O n log iteration bound for obtaining an optimal solution where n is the order of the semide nite decision variable In this paper we propose to use a di erent search direction viz the so called V space direction It is shown that this modi cation reduces the iteration complexity to O n log Independently Monteiro and Y Zhang obtained a similar result using Nesterov Todd directions