Characterizations of Tilt-Stable Local Minimizers of a Class of Matrix Optimization Problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918273521549312 |
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| author | Ding, Chao Sarabi, Ebrahim Wang, Shiwei |
| author_facet | Ding, Chao Sarabi, Ebrahim Wang, Shiwei |
| contents | Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order variational behavior, their characterization remains incomplete beyond well-known polyhedral and certain specialized nonpolyhedral settings. To help bridge this gap, we propose a new point-based criterion for tilt stability in prox-regular, subdifferentially continuous functions by exploiting the notion of minimal quadratic bundles. Furthermore, we derive an explicit formula for the minimal quadratic bundle associated with a broad class of general spectral functions, thus providing a practical and unifying framework that significantly extends existing results and offers broader applicability in matrix optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizations of Tilt-Stable Local Minimizers of a Class of Matrix Optimization Problems Ding, Chao Sarabi, Ebrahim Wang, Shiwei Optimization and Control 90C31, 49J52, 49J53 Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order variational behavior, their characterization remains incomplete beyond well-known polyhedral and certain specialized nonpolyhedral settings. To help bridge this gap, we propose a new point-based criterion for tilt stability in prox-regular, subdifferentially continuous functions by exploiting the notion of minimal quadratic bundles. Furthermore, we derive an explicit formula for the minimal quadratic bundle associated with a broad class of general spectral functions, thus providing a practical and unifying framework that significantly extends existing results and offers broader applicability in matrix optimization problems. |
| title | Characterizations of Tilt-Stable Local Minimizers of a Class of Matrix Optimization Problems |
| topic | Optimization and Control 90C31, 49J52, 49J53 |
| url | https://arxiv.org/abs/2503.03217 |