Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915374766751744 |
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| author | Ponte, Gabriel Fampa, Marcia Lee, Jon Xu, Luze |
| author_facet | Ponte, Gabriel Fampa, Marcia Lee, Jon Xu, Luze |
| contents | We present several algorithms aimed at constructing sparse and structured sparse (row-sparse) generalized inverses, with application to the efficient computation of least-squares solutions, for inconsistent systems of linear equations, in the setting of multiple right-hand sides and a rank-deficient constraint matrix. Leveraging our earlier formulations to minimize the 1- and 2,1- norms of generalized inverses that satisfy important properties of the Moore-Penrose pseudoinverse, we develop efficient and scalable ADMM algorithms to address these norm-minimization problems and to limit the number of nonzero rows in the solution. We establish a 2,1-norm approximation result for a local-search procedure that was originally designed for 1-norm minimization, and we compare the ADMM algorithms with the local-search procedure and with general-purpose optimization solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses Ponte, Gabriel Fampa, Marcia Lee, Jon Xu, Luze Optimization and Control We present several algorithms aimed at constructing sparse and structured sparse (row-sparse) generalized inverses, with application to the efficient computation of least-squares solutions, for inconsistent systems of linear equations, in the setting of multiple right-hand sides and a rank-deficient constraint matrix. Leveraging our earlier formulations to minimize the 1- and 2,1- norms of generalized inverses that satisfy important properties of the Moore-Penrose pseudoinverse, we develop efficient and scalable ADMM algorithms to address these norm-minimization problems and to limit the number of nonzero rows in the solution. We establish a 2,1-norm approximation result for a local-search procedure that was originally designed for 1-norm minimization, and we compare the ADMM algorithms with the local-search procedure and with general-purpose optimization solvers. |
| title | Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.17540 |