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

Soodeh Habibi; Arefeh Kavand; Michal Kocvara; Michael Stingl

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arXiv · 2105.08529

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

Soodeh Habibi·Arefeh Kavand·Michal Kocvara·Michael Stingl

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Abstract

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.

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Soodeh Habibi, Arefeh Kavand, Michal Kocvara, Michael Stingl. 2021-05-18. Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design. https://arxiv.org/abs/2105.08529

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