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

2021/05/18 by Soodeh Habibi, Habibi, Soodeh, Arefeh Kavand +5
Engineering · Mathematics · #65F08 #74P05 #90C22 #90C51 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Topology Optimization in Engineering

paper · doi:10.48550/arxiv.2105.08529

openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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