## A superlinearly convergent primal-dual infeasible-interior-point algorithm for
semidefinite programming LCP

### Florian Potra and Ronquin Sheng

We propose a primal-dual infeasible-interior-point path-following algorithm for solving
semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm
is globally convergent. If the starting point is feasible or close to being feasible, the
algorithms finds an optimal solution in at most $O(\sqrt{n}L)$ iterations. If the starting
point is large enough then the algorithm terminates in at most $O(nL)$ steps either by
finding a solution or by determining that the primal-dual problem has no solution of norm
less than a given number. Moreover, we propose a sufficient condition for the superlinear
convergence of the algorithm. In addition, we give two special cases of SDP for which the
algorithm is quadratically convergent.

Reports on Computational Mathematics, No.78, Department of Mathematics, The University
of Iowa, October 1995.