Loraine – an interior-point solver for low-rank semidefinite programming

Abstract

The aim of this paper is to introduce a new code for the solution of large-and-sparse linear semidefinite programs (SDPs) with low-rank solutions or solutions with few outlying eigenvalues, and/or problems with low-rank data. We propose to use a preconditioned conjugate gradient method within an interior-point SDP algorithm and an efficient preconditioner fully utilizing the low-rank information. The efficiency is demonstrated by numerical experiments using the truss topology optimization problems, Lasserre relaxations of the MAXCUT problems and the sensor network localization problems.