(eng): An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared with the so-called optimality condition method, an established technique in topology optimization. This method is also equipped with the multigrid preconditioned conjugate gradient algorithm. We conclude that, for large scale problems, the interior point method with an inexact iterative linear solver is superior to any other variant studied in the paper.