Norm constraint convexification

Hi everybody,

Lets assume we have a quadratic constrained quadratic programm (QCQP), which minimizes a cost function w.r.t. a variable x \in R^n. Now i am adding the non-convex constraint ||x||_2 \geq r, where the norm of x should be greater than the positive number r.

I am wondering which ways are availible to convexify such a non-convex constraints. At the moment i have some ideas (e.g. introducing a plane, which would restrict the solution space quite restictive) but i would like to know if there are other ways of convexification?


CVX certainly doesn’t provide an easy way, no. But you may consider this post:
How to handle nonlinear equality constraints?