Spectrally Constrained Optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918100304134144 |
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| author | Garner, Casey Lerman, Gilad Zhang, Shuzhong |
| author_facet | Garner, Casey Lerman, Gilad Zhang, Shuzhong |
| contents | We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions, i.e., $F(X) = \langle C, X \rangle$, and perform exact projections onto the eigenvalue constraint set. Two first-order algorithms are developed to obtain first-order stationary points for general non-convex objective functions. Both methods are proven to converge sublinearly when the constraint set is convex. Numerical experiments demonstrate the applicability of both the model and the methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectrally Constrained Optimization Garner, Casey Lerman, Gilad Zhang, Shuzhong Optimization and Control 90C26, 90C52, 65K10, 68W40 We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions, i.e., $F(X) = \langle C, X \rangle$, and perform exact projections onto the eigenvalue constraint set. Two first-order algorithms are developed to obtain first-order stationary points for general non-convex objective functions. Both methods are proven to converge sublinearly when the constraint set is convex. Numerical experiments demonstrate the applicability of both the model and the methods. |
| title | Spectrally Constrained Optimization |
| topic | Optimization and Control 90C26, 90C52, 65K10, 68W40 |
| url | https://arxiv.org/abs/2307.04069 |