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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08654 |
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| _version_ | 1866915242847502336 |
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| author | Gowda, M. Seetharama Sossa, David |
| author_facet | Gowda, M. Seetharama Sossa, David |
| contents | We introduce the concepts of commutativity relative to a transformation group and strong commutativity in the setting of a semi-FTvN system and show their appearance as optimality conditions in certain optimization problems. In the setting of a semi-FTvN system (in particular, in an FTvN system), we show that strong commutativity implies commutativity and observe that in the special case of Euclidean Jordan algebra, commutativity and strong commutativity concepts reduce, respectively, to those of operator and strong operator commutativity. We demonstrate that every complete hyperbolic polynomial induces a semi-FTvN system. By way of an application, we describe several commutation principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some commutation principles for optimization problems over transformation groups and semi-FTvN systems Gowda, M. Seetharama Sossa, David Optimization and Control 15A27, 17C20, 46N10, 90C33 We introduce the concepts of commutativity relative to a transformation group and strong commutativity in the setting of a semi-FTvN system and show their appearance as optimality conditions in certain optimization problems. In the setting of a semi-FTvN system (in particular, in an FTvN system), we show that strong commutativity implies commutativity and observe that in the special case of Euclidean Jordan algebra, commutativity and strong commutativity concepts reduce, respectively, to those of operator and strong operator commutativity. We demonstrate that every complete hyperbolic polynomial induces a semi-FTvN system. By way of an application, we describe several commutation principles. |
| title | Some commutation principles for optimization problems over transformation groups and semi-FTvN systems |
| topic | Optimization and Control 15A27, 17C20, 46N10, 90C33 |
| url | https://arxiv.org/abs/2503.08654 |