Gradient Descent for l1 norm

Hello every one I am new to convex optimization. I want to know why cant we use the Gradient descent for l1 norm.

my formulation is l1norm .

I am trying to solve this using gradient descent formulation.

Can some one help me with this.

This the CVX forum. None of the solvers used by CVX use gradient descent.

If you wish to discuss formulation and solution of a convex optimization problem in CVX, then this is the right place to do so. Otherwise, another forum such as or might be more appropriate.

If you want to use TFOCS, which uses first order methods, and which unlike CVX, is NOT easy to use, you can also ask for help on this forum. In such case, please choose the TFOCS category when you submit your question.