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Duality Mapping for Schatten Matrix Norms.
- Source :
-
Numerical Functional Analysis & Optimization . 2021, Vol. 42 Issue 6, p679-695. 17p. - Publication Year :
- 2021
-
Abstract
- In this paper, we fully characterize the duality mapping over the space of matrices that are equipped with Schatten norms. Our approach is based on the analysis of the saturation of the Hölder inequality for Schatten norms. We prove in our main result that, for p ∈ (1 , ∞) , the duality mapping over the space of real-valued matrices with Schatten-p norm is a continuous and single-valued function and provide an explicit form for its computation. For the special case p = 1, the mapping is set-valued; by adding a rank constraint, we show that it can be reduced to a Borel-measurable single-valued function for which we also provide a closed-form expression. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATRIX norms
*SINGULAR value decomposition
*CONTINUOUS functions
Subjects
Details
- Language :
- English
- ISSN :
- 01630563
- Volume :
- 42
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Numerical Functional Analysis & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 150938340
- Full Text :
- https://doi.org/10.1080/01630563.2021.1922438