Hi,

I need to minimize an objective function that has multiple norms in it.

Here is a minimal example:

A is a variable of dimension d by n.

x is a known constant matrix of dimension n by 1 and b_t (dimension d by 1) is the data gathered with iterations. A0 is a known constant matrix of dimension d by n

The objective function is: `Σ_{s=1}^{t}norm(A*x-b_t)^2+norm(A-A0)^2`

. `Σ_{s=1}^{t}`

means sum from s =1 to s = t.

Suppose t is 3 and we know b_1,b_2,b_3.

We need the find the A that minimizes the objective function.

How should we construct the model using JuMP?

Here is the code i have:

```
using Ipopt
using JuMP
model = Model(Ipopt.Optimizer)
@variable(model, A[1:d, 1:n])
objective = 0.0
for s = 1:t
objective = objective + norm(A*x-b[t])^2+norm(A-A0)^2
end
@NLobjective(model, Min, objective)
JuMP.optimize!(model)
```