After producing the objective function and gradient with TMB, and calling the optim function, I get a sequence of reports printed in my console that seems to of the form "outer mgc: ":
outer mgc: 56.54273
outer mgc: 56.51064
outer mgc: 56.96065
outer mgc: 57.13384
outer mgc: 29.01959
outer mgc: 27.08267
outer mgc: 25.99866
outer mgc: 25.79068
outer mgc: 25.58621
outer mgc: 21.91722
outer mgc: 21.73952
outer mgc: 21.56449
outer mgc: 21.52924
outer mgc: 21.52189
outer mgc: 21.19551
outer mgc: 20.7331
outer mgc: 16.39087
outer mgc: 11.35111
outer mgc: 10.61466
outer mgc: 6.748524
outer mgc: 1.420802
outer mgc: 0.1197647
It seems that smaller numbers indicate quicker convergence and better convergence results. But I am not entirely sure what these are so it would be nice to know in order to diagnose the convergence properties of the algorithm.
The abbreviation mgc stands for "maximum gradient component".
For each parameter TMB estimates a gradient (partial derivative), which after optimisation you can get by running obj$gr(opt$par). All of these should be as close to zero as possible. So for the model to be ok, the highest or maximum one (furthest away from zero) should still be low. You'll notice that when using sdreport(), the final maximum gradient component is also given. These gradients are by default also calculated and printed (unless silent=TRUE in makeADfun) for each iteration when using nlminb/optim.