Abstract
This letter develops a distributed optimization framework for solving the rank-constrained semidefinite programs (RCSPs). Since the rank constraint is non-convex and discontinuous, solving an optimization problem with rank constraints is NP-hard and notoriously time-consuming, especially for large-scale RCSPs. In the proposed approach, by decomposing an unknown matrix into a set of submatrices with much smaller sizes, the rank constraint on the original matrix is equivalently transformed into a set of constraints on the decomposed submatrices. The distributed framework allows parallel computation of subproblems while requiring coordination among them to satisfy the coupled constraints. As the scale of every subproblem solved independently is significantly reduced, the decomposition scheme and the distributed framework can be applied to large-scale RCSPs. Moreover, optimality conditions of the proposed distributed optimization algorithm for RCSPs at the converged point are analyzed. Finally, the efficiency and effectiveness of the proposed method are demonstrated via simulation examples for solving the image denoising problem.
Recommended Citation
C. Pei et al., "Distributed Optimization for Rank-Constrained Semidefinite Programs," IEEE Control Systems Letters, vol. 7, pp. 103 - 108, Institute of Electrical and Electronics Engineers, Jan 2023.
The definitive version is available at https://doi.org/10.1109/LCSYS.2022.3186939
Department(s)
Mechanical and Aerospace Engineering
Keywords and Phrases
Distributed optimization; Rank-constrained optimization
International Standard Serial Number (ISSN)
2475-1456
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Jan 2023
