Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming

Two primal{dual a ne scaling algorithms for linear programming are extended to semide nite programming. The algorithms do not require (nearly) centered starting solutions, and can be initiated with any primal{dual feasible solution. The rst algorithm is the Dikin-type a ne scaling method of Jansen et al. [8] and the second the pure a ne scaling method of Monteiro et al. [12]. The extension of the former has a worst-case complexity bound of O( 0nL) iterations, where 0 is a measure of centrality of the the starting solution, and the latter a bound of O( 0nL2) iterations.