How to get W* form minimize function

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I need help to solve this equation

$$\min_{W} ||XW-X||_F^2+p_1||W||_1+p_2R(W), W>=0$$ X size dxn (d = number of feature & n = number of data)
Example input:
X is random matrix 3x5 $$R(W)=Tr(W^TX^TLXW)$$ L = laplacian matrix
Close solution W $$W=(X^TX+pI)^-1+X^TX$$ Result:
W* (W* is matrix nxn/5x5)

For complete journal : http://www.massey.ac.nz/~rwang/publications/17-TNNLS-Zhang.pdf