mcg’s answer is correct; the problem is not convex, and cannot be expressed in DCP format. more specifically, a constraint like \|Aw\|_2 \leq P (with A a constant matrix and w a variable) is OK (convex, and DCP), but the converse constraint, \|Aw\|_2 \geq P, is not convex, and (therefore) not DCP.

i’d like to add that there are heuristic methods for “handling” such problems, using the so-called convex-concave procedure (see EE364b, lecture on sequential convex programming). this is a heuristic method, that uses convex optimization as a subroutine, to “solve” problems like this one. heuristic means the method can fail; the w found need not be the global solution. but such methods can work well in practice.

for a reverse norm inequality like this, the method works as follows. we replace \|Aw\|_2 \geq P with the convex (and DCP) constraint q^T(Aw) \geq P, where q=(Aw^\mathrm{prev})/\|Aw^\mathrm{prev}\|_2, where w^\mathrm{prev} is the value of w at the last iteration. solving the resulting convex problem gives us the new value of w. (you must start with a nonzero value of w. in fact, you might start the convex-concave procedure with several different values of w; you could well get different final results.)

our experience is that this works quite well in practice. but remember that this method does not find the global solution.