Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming

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Autores principales:	Bottazzi, Tamara Paula, Varela, Alejandro
Formato:	Artículo publishedVersion
Lenguaje:	Inglés
Publicado:	Elsevier Science 2026
Materias:	Minimal operators Subdifferential of Eigenvalues Moment of a subspace Semi-definite Programming Matemáticas
Acceso en línea:	http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2696
Aporte de:	Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento

id	I71-R177-UNGS-2696
record_format	dspace
spelling	I71-R177-UNGS-26962026-01-14T11:37:27Z Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming Bottazzi, Tamara Paula Varela, Alejandro Minimal operators Subdifferential of Eigenvalues Moment of a subspace Semi-definite Programming Matemáticas Revista con referato Fil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina. Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Formulamos la cuestión de la minimalidad de los operadores autoadjuntos en un espacio de Hilbert complejo como un problema semidefinido, vinculando el trabajo de Overton en cite{overton} con la caracterización de matrices hermíticas minimales. Esto nos motiva a investigar la relación entre los operadores autoadjuntos minimales y el subdiferencial del autovalor máximo, inicialmente para matrices y posteriormente para operadores compactos. Para ello, obtenemos nuevas fórmulas de subdiferenciales de autovalores máximos de operadores compactos que resultan útiles en estos problemas de optimización. Además, proporcionamos fórmulas para la minimización de diagonales de operadores autoadjuntos de rango uno, un resultado que podría aplicarse a la optimización numérica de autovalores a gran escala. We formulate the issue of minimality of self-adjoint operators on a complex Hilbert space as a semi-definite problem, linking the work by Overton in cite{overton} to the characterization of minimal hermitian matrices. This motivates us to investigate the relationship between minimal self-adjoint operators and the subdifferential of the maximum eigenvalue, initially for matrices and subsequently for compact operators. In order to do it we obtain new formulas of subdifferentials of maximum eigenvalues of compact operators that become useful in these optimization problems.Additionally, we provide formulas for the minimizing diagonals of rank one self-adjoint operators, a result that might be applied for numerical large-scale eigenvalue optimization. 2026-01-14T11:37:26Z 2026-01-14T11:37:26Z 2025 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Bottazzi, T. P. y Varela, A. (2025). Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming. Linear Algebra and its Applications, (716), 1-31. 0024-3795 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2696 eng http://dx.doi.org/10.1016/j.laa.2025.03.017 info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier Science Linear Algebra and its Applications. Jul. 2025; (716): 1-31 https://www.sciencedirect.com/journal/linear-algebra-and-its-applications/vol/716/suppl/C
institution	Universidad Nacional de General Sarmiento
institution_str	I-71
repository_str	R-177
collection	Repositorio Institucional Digital de Acceso Abierto (UNGS)
language	Inglés
orig_language_str_mv	eng
topic	Minimal operators Subdifferential of Eigenvalues Moment of a subspace Semi-definite Programming Matemáticas
spellingShingle	Minimal operators Subdifferential of Eigenvalues Moment of a subspace Semi-definite Programming Matemáticas Bottazzi, Tamara Paula Varela, Alejandro Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
topic_facet	Minimal operators Subdifferential of Eigenvalues Moment of a subspace Semi-definite Programming Matemáticas
description	Revista con referato
format	Artículo Artículo publishedVersion
author	Bottazzi, Tamara Paula Varela, Alejandro
author_facet	Bottazzi, Tamara Paula Varela, Alejandro
author_sort	Bottazzi, Tamara Paula
title	Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
title_short	Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
title_full	Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
title_fullStr	Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
title_full_unstemmed	Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
title_sort	minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming
publisher	Elsevier Science
publishDate	2026
url	http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2696
work_keys_str_mv	AT bottazzitamarapaula minimalcompactoperatorssubdifferentialofthemaximumeigenvalueandsemidefiniteprogramming AT varelaalejandro minimalcompactoperatorssubdifferentialofthemaximumeigenvalueandsemidefiniteprogramming
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Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming

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