Simple convex optimization problem

[Normen]

Hi all,

I need to solve something of the form

min_x  ||Ax-b||_2^2 

s.t. ||F_1(x)-F_2(x)||_2^2 < epsilon

Where x is a vector, A is a matrix, and F1 and F2 are operators (functions) that take the vector x and compute certain number out of it. 
I'd like to solve this problem without having to know the adjoints of F1 and F2 (the don't have an adjoint). 

Anyone has an idea if this is possible using CVXOPT? 

Thanks,

Normen

[Martin]

Generally speaking, the problem cannot be solved with CVXOPT. If F_1 and F_2 are mappings from R_n to R, then your constraint is equivalent to

-sqrt(epsilon) < F_1(x) - F_2(x) < sqrt(epsilon) 

and hence F_1 and F_2 must be linear operators in order for the feasible set to be convex.