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On Computing Sparse Generalized Inverses and Sparse-Inverse/Low-Rank Decompositions
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | On Computing Sparse Generalized Inverses and Sparse-Inverse/Low-Rank Decompositions. |
| 개인저자 | Fuentes, Victor K. |
| 단체저자명 | University of Michigan. Industrial & Operations Engineering. |
| 발행사항 | [S.l.]: University of Michigan., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 115 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-05B. Dissertation Abstract International |
| ISBN | 9781687934871 |
| 학위논문주기 | Thesis (Ph.D.)--University of Michigan, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Advisor: Lee, Jon. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using 1-norm minimization and linear programming. We introduce several new sparse generalized inverses by using 1-norm minimization on a subset of the linear Moore-Penrose properties, again leading to linear programming. Computationally, we demonstrate the usefulness of our approach in the context of application to least-squares problems and minimum 2-norm problems. One of the Moore-Penrose properties is nonlinear (in fact, quadratic), and so developing an effective convex relaxation for it is nontrivial. We develop a variety of methods for this, in particular a nonsymmetric lifting which is more efficient than the usual symmetric lifting that is normally applied to non-convex quadratic equations. In this context, we develop a novel and computationally effective "diving procedure" to find a path of solutions trading off sparsity against the nice properties of the Moore- Penrose pseudoinverse. Next, we consider the well-known low-rank/sparse decomposition problemmin {. |
| 일반주제명 | Operations research. Mathematics. Engineering. |
| 언어 | 영어 |
| 바로가기 | 
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