This is actually a convex problem. Or more specifically, with this input data, can be rewritten as a convex problem.

First of all, `norm.(..)^2`

needs to be replaced by `square_pos(norm(...))`

.

Second of all, as I wrote in my previous reply:

` I don’t understand why l(p) <= norm(X{p},1) would be accepted by CVX, because it si a non-convex constraint. Even if l(p) were zero, CVX still would reject it, even though in that case it would be a vacuous constraint which some optimization modeling system could eliminate, but CVX does not.`

Indeed, CVX does not accept this. But given that `l`

is the zero vector, that constraint can be removed as vacuous. Therefore, the problem can be rewritten as below, and it is successfully solved. But it is not a homogeneous problem; and CVX solves it by calling a solver. not analytically.

```
cvx_begin
variable x(n)
f = dot(alpha_v,x.^2) + dot(beta_v,x)+transpose(v)*x+rho/2*square_pos(norm(Nabla*x));
minimize f
subject to
norm(x,1) <= u(1);
cvx_end`
```

In the future, please make sure that the output you show corresponds to the program you show, which obviously was NOT the case in your post.