# Nuclear norm minimization of a matrix in the presence of non-negativity constraints [duplicate]

This question already has an answer here:

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 UnknownJul 7 at 5:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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