The dimension of Y \in R^{M \times L}, W \in R^{M \times R} and H \in R^{R \times L} w_i and w_j are the i^{th} and j^{th} columns of matrix W.
Given : Y, H, and \lambda
The optimization problem:

\min_{W} ||Y - W * H ||{_F^2} + \lambda \sum_{i \neq j} |w_i^T * w_j|

How to formulate this problem in cvx. Kindly help.

Thank you, sir. Yes, sir, I have seen my earlier thread. Is there any way to update the problem so that becomes convex. I have been struggling with this problem for a long time.

You can solve a different problem, such as LASSO, which is convex. If you really want to solve the problem specified, you will have to use a non-convex solver. and will not be able to use CVX.

I was referring to the FAQ linked in the answer in your earlier tread, and which I linked to in my first answer in this thread. I suggest you read it, carefully.