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The aim of this paper is to solve large-and-sparse linear SemidefinitePrograms (SDPs) with low-rank solutions. We propose to use a preconditionedconjugate gradient method within second-order SDP algorithms and introduce anew efficient preconditioner fully utilizing the low-rank information. Wedemonstrate that the preconditioner is universal, in the sense that it can beefficiently used within a standard interior-point algorithm, as well as a newlydeveloped primal-dual penalty method. The efficiency is demonstrated bynumerical experiments using the truss topology optimization problems of growingdimension.

Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design