Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras
| dc.contributor.author | Gowda, Muddappa | |
| dc.date.accessioned | 2020-11-03T16:33:19Z | |
| dc.date.available | 2020-11-03T16:33:19Z | |
| dc.date.issued | 2020-09-10 | |
| dc.description.abstract | The commutation principle of Ramirez, Seeger, and Sossa proved in the setting of Euclidean Jordan algebras says that when the sum of a real valued function h and a spectral function Φ is minimized/maximized over a spectral set E, any local optimizer a at which h is Fréchet differentiable operator commutes with the derivative h′(a). In this paper, assuming the existence of a subgradient in place the derivative (of h), we establish `strong operator commutativity' relations: If a solves the problem maxE(h+Φ), then a strongly operator commutes with every element in the subdifferential of h at a; If E and h are convex and a solves the problem minEh, then a strongly operator commutes with the negative of some element in the subdifferential of h at a. These results improve known (operator) commutativity relations for linear h and for solutions of variational inequality problems. We establish these results via a geometric commutation principle that is valid not only in Euclidean Jordan algebras, but also in the broader setting of FTvN-systems. | en_US |
| dc.description.uri | https://arxiv.org/abs/2009.04874 | en_US |
| dc.format.extent | 10 pages | en_US |
| dc.genre | conference papers and proceedings preprints | en_US |
| dc.identifier | doi:10.13016/m2wuxm-fwbn | |
| dc.identifier.citation | Muddappa Gowda, Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras, https://arxiv.org/abs/2009.04874 | en_US |
| dc.identifier.uri | http://hdl.handle.net/11603/20000 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.title | Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras | en_US |
| dc.type | Text | en_US |