Your problem Is not convex. Consider the special case in which w is a real scalar.variable, Then \|w\|/(\|w\|+\epsilon) is concave for any \epsilon > 0. Therefore, your function can not be convex.

Did you perhaps find this in a paper which proposed a successive convex programming solution? For instance, start off with a starting value value (guess) for w. Then call CVX (convex solver) iteratively within a do while loop, each time replacing w in the denominator with its value form the previous iteration (starting value for first time though loop)? Each of these problems can easily be entered into CVX and solved, then w in the denominator is updated for the next iteration. I think there a problem along these lines posted to this forum some time ago.

There may not be a guarantee that this iterative scheme will converge to any answer, let alone a local minimum, let alone the global minimum. And its performance could heavily depend on the starting value chosen for w in the denominator…