A projective method of the approximate center for semidefinite programming

Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, the author extends Roos's projective method for linear programming to SDP. The method is path-following and based on the use of a multiplicative barrier function. The iteration bound depends on the choice of the exponent μ in the numerator of the barrier function. The analysis in this paper resembles that of the approximate center method for linear programming, as proposed by Roos and Vial.