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How to maximum L1 norm problem?

I have met a problem these days. \begin{equation} \underset{\omega}{\max} \quad \Vert \text{diag}(\mathbf{h}^H)\mathbf{G}^H\mathbf{\omega}\Vert_1 \\ s.t.\quad\mathbf{\omega}^H\mathbf{G}\mathbf{G}^H\...
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