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Duality Mapping for Schatten Matrix Norms

S. Aziznejad, M. Unser

Numerical Functional Analysis and Optimization, vol. 42, no. 6, pp. 679–695, 2021.

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.

@ARTICLE(http://bigwww.epfl.ch/publications/aziznejad2103.html,
AUTHOR="Aziznejad, S. and Unser, M.",
TITLE="Duality Mapping for {S}chatten Matrix Norms",
JOURNAL="Numerical Functional Analysis and Optimization",
YEAR="2021",
volume="42",
number="6",
pages="679--695",
month="",
note="")

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