最小紧算子，最大特征值的次微分和半定规划

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-03-25 DOI:10.1016/j.laa.2025.03.017

Tamara Bottazzi , Alejandro Varela

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引用次数: 0

摘要

我们将复希尔伯特空间上自伴随算子的极小性问题表述为一个半定问题，将Overton在[18]中的工作与极小厄米特矩阵的表征联系起来。这促使我们研究最小自伴随算子和最大特征值的子微分之间的关系，首先是矩阵，然后是紧算子。为了做到这一点，我们得到了紧算子最大特征值的子微分的新公式，这些公式在这些优化问题中很有用。此外，我们还提供了一阶自伴随算子的最小对角线的计算公式，该结果可用于数值大规模特征值优化。

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

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 [18] 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.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.