Some commutation principles for optimization problems over transformation groups and semi-FTvN systems
Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
DOI: 10.13016/m2ko3o-gaxh
Authors: Gowda, M. Seetharama, Sossa, David
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6884864692
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