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How can I solve this maximization problem with inequality constraint on the Frobenius norm?
$$
\max_{C\in \mathbb{S}^n} x^TCx\\
s.t. \|C\|_{tr}^2\leq b
$$
where $\|C\|_{tr}^2=tr(C^TC)=tr(CC)$, $C$ is a symmetric matrix.
- 11
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Maximize $\langle \mathrm A , \mathrm X \rangle$ subject to $\| \mathrm X \|_F = 1$
Given $\mathrm A \in \mathbb R^{m \times n}$,
$$\begin{array}{ll} \text{maximize} & \langle \mathrm A , \mathrm X \rangle\\ \text{subject to} & \| \mathrm X \|_F = 1\end{array}$$
I can think ...
