I want to solve the minimization problem min(norm(y-Af,2)^2+lambda*norm(d(abs(f))/dx,1))

where y, f are complex vectors, A is a complex matrix, lambda is a constant.

when f=[f1, f2, … , fn], d(abs(f))/dx can be expressed as d(abs(f))/dx=[abs(f1)-abs(f2),abs(f2)-abs(f3),…,abs(fn-1)-abs(fn)].

So, when I run this problem in CVX

cvx_begin

variable f(n) complex;

expressions f_dx1(n-1) f_dx2(n-1);

f_dx1=f(1:n-1);

f_dx2=f(2:n);

minimize( sum_square_abs(A * f-y)+lambda * (norm(abs(f_dx1)-abs(f_dx2),1)) );

cvx_end

I received an error that {convex} - {convex}.

abs(f_dx1) - abs(f_dx2) is not convex. but norm(abs(f_dx1)-abs(f_dx2),1) is convex.

How can I express this convex problem so that it can be executed in cvx?