  The aim of this paper is to solve large-and-sparse linear Semidefinite
Programs (SDPs) with low-rank solutions. We propose to use a preconditioned
conjugate gradient method within second-order SDP algorithms and introduce a
new efficient preconditioner fully utilizing the low-rank information. We
demonstrate that the preconditioner is universal, in the sense that it can be
efficiently used within a standard interior-point algorithm, as well as a newly
developed primal-dual penalty method. The efficiency is demonstrated by
numerical experiments using the truss topology optimization problems of growing
dimension.
