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

Soodeh Habibi (1) , Arefeh Kavand (2) , Michal Kocvara (1) , Michael Stingl (2)

1 School of Mathematics, University of Birmingham
2 Department Mathematik [Erlangen]

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.

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Soodeh Habibi, Arefeh Kavand, Michal Kocvara, Michael Stingl. Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design. 2021. ⟨hal-03229944⟩