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 https://groups.google.com/forum/#!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

precision.

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.

Thank you