I think if you can spare a slide on what the aim of robust statistics is, it may be helpful. The paper presents how least squares can be robustified and mentions outlier, but not the general idea.

The Jacobian and Hessian matrices in a bundle problem seems to be different and problem specific as compared to an ordinary optimization problem. It so happens that H is structured such that each entry gives a relationship between row and column indices. If, then we wanted to use third order derivatives in our system (assuming we have an optimization algorithm that uses these third order derivatives), then I think we would have to consider 3D matrices. Has anyone seen seen such an application or optimization algorithm?

Also, it is mentioned in the paper that relationships between different features (inter-feature measurements such as angles) are not included to the H in the example on page 20. But I would argue that inclusion of such relationships bring correlation problems. How would this be solved? (If anyone can point me to any reference, that would be fine too.)