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Let $L$ and $R$ be $n \times n$ matrices. Consider the following minimization problem

\begin{equation} \mathbf{L} = \min_{L \geq \mathbf{0}} \mu\|\mathbf{L}\|_* + \dfrac{1}{2\lambda}\|\mathbf{L-R}\|_F^2 \end{equation}

By $\mathbf{L}$ $\geq$ 0 , i mean that i wish the entries of $\mathbf{L}$ to be non negative. I know the solution can be obtained using the singular value thresholding of $\mathbf{R}$ when the non-negativity constraint on $\mathbf{L}$ is not present. But I can't figure out the change needed in order to satisfy the non-negativity constraint on $\mathbf{L}$. Will simply setting the negative entries of $\mathbf{L}$ to zero work? This link How to solve this minimization problem involving the nuclear norm? is about $\mathbf{L}$ being positive definite; my question is about the entries of $\mathbf{L}$ being non-negative. Can someone please answer this?


marked as duplicate by YuiTo Cheng, Lee David Chung Lin, Shailesh, The Count, Lord Shark the Unknown Jul 7 at 5:01

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    $\begingroup$ $L \succeq O$ is not a non-negativity constraint. $\endgroup$ – Rodrigo de Azevedo Jul 6 at 10:55
  • $\begingroup$ I want the entries in $\mathbf{L}$ to be non negative.. i did not mean $\mathbf{L}$ to be positive semi definite.. $\endgroup$ – sourish Jul 6 at 18:07
  • $\begingroup$ Can simply setting the negative entries of $\mathbf{L}$ to zero work? $\endgroup$ – sourish Jul 6 at 18:12
  • $\begingroup$ @RyanCory-Wright The link talks about $\mathbf{L}$ being positive definite. My concern is different. I want the entries of $\mathbf{L}$ to be non negative.. $\endgroup$ – sourish Jul 7 at 4:37