A new solver for robustified non-linear least squares problems, with non-Euclidean variables

I have written a new solver for robustified non-linear least squares problems, with non-Euclidean variables. It can compute auto-differentiated Jacobians when necessary. I have called the package NLLSsolver. Please feel free to clone it from GitHub and try it out. Feedback is welcomed.

Until recently I prototyped in MATLAB, and wrote production code in C++. I have been following Julia for a while, as a potential replacement for both. Recently I decided to try it out, and since I tend to do a lot of non-linear least squares optimizations of geometry problems in my work, my first goal was to optimize bundle adjustment (BA) problems.

I first had a look at existing Julia optimizer frameworks, JuMP and NLPModels. I found an implementation of BA as an NLPModel. However, I found that the model did not support robustification (necessary for downweighting outlier or erroneous measurements), did not seem able to model non-Euclidean variables such as 3D rotation matrices, and also had hand-coded derivatives (I’m not sure if auto-differentiation (AD) was or is now available). I needed to be able to do all 3 of these things. In addition, I was put off JuMP by the assessment of the authors of that BA implementation, who made it sound even less suitable.

This led me to decide to implement my own optimization framework for robustified non-linear least squares problems. It’s been a very interesting first major project in Julia for me, and now I’m ready to share it publicly. It’s still in the early stages, and there isn’t much documentation (just the readme, and file comments), but there are a couple of examples, BA being one of them. I tested it against the NLPModels BA optimization on an unrobustified problem, and it was competitive (actually slightly faster, reaching the same cost), despite having auto-differentiated derivatives instead of hand-coded ones. There’s also still huge scope for reducing allocations.

Many thanks to everyone who has answered my questions on this forum since I started learning Julia. Hopefully I can now give a bit back to the community.