I’d like to track loss values in a particle swarm optimization with a callback, but I’m not sure where exactly the loss numbers being tracked in the callback are coming from.

Comparing the trace printed by the optimizer to the loss kept through the callback, the minimum callback-tracked loss does not match the minimum reported by the optimizer.

Here’s an adaptation of this example.

```
using ModelingToolkit, Optimization, OptimizationOptimJL
@variables x y
@parameters a b
loss = (a - x)^2 + b * (y - x^2)^2
loss_list = []
cb = function(x,loss)
append!(loss_list,loss)
false
end
@named sys = OptimizationSystem(loss,[x,y],[a,b])
guess = [
x=>rand(1e-3 : 1e-3 : 1e1)
y=>rand(1e-3 : 1e-3 : 1e1)
]
p = [
a => 6.0
b => 7.0
]
lower = [ 0.0, 0.0]
upper = [100.0, 100.0]
prob = OptimizationProblem(sys, guess, p, lb=lower, ub=upper)
# prob2 = OptimizationProblem(sys,u0,p,grad=true,hess=true)
swarm_population = 100
max_iters = 100
sol = solve(prob,ParticleSwarm(n_particles=swarm_population),maxiters=max_iters,callback=cb, show_trace=true)
# sol2 = solve(prob2,Newton(),show_trace=true,callback=cb)
(opt_loss_val, opt_loss_idx) = findmin(loss_list)
println("Min loss in callback: $(opt_loss_val), found in iteration $(opt_loss_idx)")
```

```
...
98 5.241673e-05 NaN
* time: 0.34200000762939453
* x: [6.007239919639608, 36.086924970333264]
99 2.757162e-05 NaN
* time: 0.3430001735687256
* x: [6.0046714866642885, 36.056985898084605]
100 2.757162e-05 NaN
* time: 0.3450000286102295
* x: [6.0046714866642885, 36.056985898084605]
Min loss in callback: 5.236272445010206e-5, found in iteration 99
```