Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian
Spectral operators of matrices proposed recently in [C. Ding, D. F. Sun, J. Sun, and K. C. Toh, Math. Program., 168 (2018), pp. 509{531] are a class of matrix-valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying...
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
SIAM PUBLICATIONS
2020
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/91436 |
| _version_ | 1848765520168353792 |
|---|---|
| author | Ding, C. Sun, D. Sun, Jie Toh, K.C. |
| author_facet | Ding, C. Sun, D. Sun, Jie Toh, K.C. |
| author_sort | Ding, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Spectral operators of matrices proposed recently in [C. Ding, D. F. Sun, J. Sun, and K. C. Toh, Math. Program., 168 (2018), pp. 509{531] are a class of matrix-valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems that include semidefinite programming as one of most important example classes. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, ρ-order B(ouligand)-differentiability (0 < ρ≤ 1), ρ-order G-semismoothness (0 < ρ≤ 1), and characteriza- tion of generalized Jacobians. |
| first_indexed | 2025-11-14T11:36:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-91436 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:33Z |
| publishDate | 2020 |
| publisher | SIAM PUBLICATIONS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914362023-04-20T06:26:02Z Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian Ding, C. Sun, D. Sun, Jie Toh, K.C. Science & Technology Physical Sciences Mathematics, Applied Mathematics spectral operators matrix-valued functions semismoothness generalized Jacobian AUGMENTED LAGRANGIAN METHOD NEWTON METHOD CONSTRAINT NONDEGENERACY NONSMOOTH ANALYSIS SINGULAR-VALUES ERROR-BOUNDS SEMIDEFINITE RANK STABILITY COMPLEMENTARITY Spectral operators of matrices proposed recently in [C. Ding, D. F. Sun, J. Sun, and K. C. Toh, Math. Program., 168 (2018), pp. 509{531] are a class of matrix-valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems that include semidefinite programming as one of most important example classes. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, ρ-order B(ouligand)-differentiability (0 < ρ≤ 1), ρ-order G-semismoothness (0 < ρ≤ 1), and characteriza- tion of generalized Jacobians. 2020 Journal Article http://hdl.handle.net/20.500.11937/91436 10.1137/18M1222235 English SIAM PUBLICATIONS fulltext |
| spellingShingle | Science & Technology Physical Sciences Mathematics, Applied Mathematics spectral operators matrix-valued functions semismoothness generalized Jacobian AUGMENTED LAGRANGIAN METHOD NEWTON METHOD CONSTRAINT NONDEGENERACY NONSMOOTH ANALYSIS SINGULAR-VALUES ERROR-BOUNDS SEMIDEFINITE RANK STABILITY COMPLEMENTARITY Ding, C. Sun, D. Sun, Jie Toh, K.C. Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title | Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title_full | Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title_fullStr | Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title_full_unstemmed | Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title_short | Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian |
| title_sort | spectral operators of matrices: semismoothness and characterizations of the generalized jacobian |
| topic | Science & Technology Physical Sciences Mathematics, Applied Mathematics spectral operators matrix-valued functions semismoothness generalized Jacobian AUGMENTED LAGRANGIAN METHOD NEWTON METHOD CONSTRAINT NONDEGENERACY NONSMOOTH ANALYSIS SINGULAR-VALUES ERROR-BOUNDS SEMIDEFINITE RANK STABILITY COMPLEMENTARITY |
| url | http://hdl.handle.net/20.500.11937/91436 |