What is the subgradient of a special composite nuclear norm?

Asked Apr 11 '25 at 09:22

Active Apr 11 '25 at 20:53

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Let $f(X)=\lVert UXV\rVert_*$ with $U^TU=I_m$ and $V^TV=I_n$. What is the subgradient $\partial f(X)$?

I don't know whether the answer is simply generated by the subgradient of nuclear norm, i.e., $$\partial f(X) = U^T\partial \lVert UXV^T\rVert_* V ?$$

edited Apr 11 '25 at 20:53

Rodrigo de Azevedo

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asked Apr 11 '25 at 09:22

zhenting luan

1

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Apr 11 '25 at 09:32
Related – Rodrigo de Azevedo Apr 11 '25 at 20:54
Related – Rodrigo de Azevedo Apr 11 '25 at 20:55

What is the subgradient of a special composite nuclear norm?

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