Numerical Solver Based Issues :The model becomes unbounded with higher 1-norm of signal

since the above model can’t be directly written, it is transformed into:
sum( Ax - 2 * ( sqrt(y) .* sqrt(Ax) ) ) + lambda * norm( x, 1 )

What is your actual question? Are you just quoting the write-up from someone else’s work, or have you tried this yourself? Have you tired alternative solvers? If you have access to MOSEK, you may find that it can deal better with models which are not numerically nice than SeDuMi or SDPT3 can, but it can not work magic either.

In general, if the numerical inputs to the solver get too extreme or have too wide a dynamic range, the solvers might have numerical difficulty and may not produce reliable results.

You have not provided reproducible inputs, to include values of y and A, so it is difficult to be much more specific.

This whole thing is my work, and have tried myself. I tried MOSEK. With CVX_precision LOW; I am able to get results but no success when precision is high or best.

Per @Erling at!topic/yalmip/osvism-XHR4

I would suggest using MOSEK version 8. That usually provide better accuracy than version 7.

If that does not help then I suggest you think about how you model
things. Is the scaling right for instance. Next you can try to change
the MOSEK tolerances but in most cases it will no effect. Since MOSEK
tends to report as accurate solution it can. MOSEK cannot solve problem
to arbitrary high accuracy since all computations are done finite

In other words the need to change the solver tolerances is often a consequence of a bad model.

What does sqrt(Ax) means. sqrt of each element of Ax.

Sorry for late response. My email notification were Off I guess. I used MOSEK 7 with CVX_Low_Precision. It gave me fair results. Although for higher tolerance values as in High/Best and sometimes Default precision of CVX, the problem seem to breakdown as infeasible/unbounded.

yes sqrt(Ax) means sqrt of each element of Ax. Similarly for y.

@Erling @Mark_L_Stone

Thank you