Interior-Point Newton tries points outside of the constraint set

[baggepinnen]

I’m not sure how Optim’s interior-point method works, but you might find this post informative

OptimizationMOI Ipopt violating inequality constraint

That is a frequent misconception. If a problem has a constraint g(x) \leq 0, for an interior-point method to ensure satisfaction of the constraint throughout, it would have to penalize g(x) in the logarithmic barrier. However, that’s not what IPOPT does. Firstly, IPOPT adds slack variables s to transform the constraint to g(x) + s = 0 and s \geq 0. Secondly, the inequality on s is penalized via the log barrier, i.e., s > 0 (strictly) is maintained throughout. BUT g(x) + s = 0 is NOT maintained…