Support of sqrt or norm

[oameye]

I need to minimize the lagrangian $\int_0^T \lVert u \rVert \lVert f(x) \rVert - \langle u , f(x) \rangle \mathrm{d}s$.
Is their anyway to do this in the OptimalControl.jl package. For the first term I need norm or sqrt. But that doesn't seem supported.

[ocots]

@oameye The optimal control problem is discretized by OptimalControl.jl and then modeled with ADNLPModels.jl (for automatic differentiation) which do no support norm nor sqrt apparently.

@jbcaillau Do we have some references explaining this?

[jbcaillau]

@oameye @ocots hi; both can indeed cause problem for AD since none of them are differentiable at zero. Having a look at it in the framework of #384 (comment) then coming back to this (more general) issue. my first thought is to replace norm(x) by sth a regularised (both symmetrised and smoothed) version of sqrt, typically by asqrt(x' * x). (though this currently raises some AD issues...)