Dear John,
My name is Rafael and I'm MSc student in São Paulo State University (Brazil). I've been solving energy systems optimization problems (MINLP/NLP) using the GEKKO package (solvers APOPT and IPOPT) and evolutionary computing.
However, until now, I didn't find any articles, videos or websites that could give me information about the mathematical details from the APOPT solver.
I've read so far:
- Hedengren, J. D. and Asgharzadeh Shishavan, R., Powell, K.M., and Edgar, T.F., Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers and Chemical Engineering, Volume 70, pg. 133–148, 2014, doi: 10.1016/j.compchemeng.2014.04.013. https://apmonitor.com/wiki/index.php/Main/APMonitorReferences (see preprint link at the top and Section 7, Figure 8 in the paper).
- Hedengren, J.D., Mojica, J.L., Cole, W., Edgar, T.F., APOPT: MINLP Solver for Differential Algebraic Systems with Benchmark Testing, INFORMS Annual Meeting, Phoenix, AZ, Oct 2012. https://apm.byu.edu/prism/uploads/Members/minlp_apopt_informs2012.pdf
- Beal, L.D.R., Hill, D., Martin, R.A., and Hedengren, J. D., GEKKO Optimization Suite, Processes, Volume 6, Number 8, 2018, doi: 10.3390/pr6080106.
I only know that it uses Branch and Bound with Active-Set Sequential Quadratic Programming.
In order to properly cite the solver in my thesis (with a comprehensive explanation about how it works) I would like to know if you have more detailed references about the APOPT or could indicate me other references/books/articles that have further explanations about the Active-Set SQP algorithm that the solver uses to solve the NLP problems.
Best Regards,
Rafael.