How to solve my second order cone problem? Thanks

My problem is following:

minimize objective function: x’Qx+c’x, where x is a 3-dim vector, Q is positive definite, c is a known vector.

constraint: x2^2+x3^2<=x1^2,x1+x2>=0 and x1-x2>=0, where x1,x2,x3 are elements of x, i.e.

How to solve this problem? Does cvx give a gloabl optim?

Thanks a lot.