SLSQP - explanation of the algorithm.

[Bartłomiej Rak]

Dear all,

I am a Master's Thesis student currently working with a python-based modelling tool for wind farm optimization, in which the recommendended optimization method is SLSQP. I have some basic background in optimization, however, SLSQP is something new to me and I am very keen on learning how it works. I did my research in the internet, studied the papers of D. Kraft "A software package for sequential quadratic programming" 1998, "Algorithm 733: TOMP - Fortran modules for optimal control calculations" 1994, read about SLSQP here: http://degenerateconic.com/slsqp/ and brushed through the codes provided here: http://jacobwilliams.github.io/slsqp/ (only intuitively, I have no knowledge of Fortran).

Unfortunately, the abovementioned sources of knowledge do not make it completely clear to me how the algorithm actually works.

To keep it short, I am trying to answer such questions:

1. What does "Sequential" stand for in this particular method?

2. What is done with the use of "Least Squares" method within SLSQP?

3. How does the algorithm avoids ending in a local minimum?

4. How it determines the search direction and the step size?

I would greatly appreciate a bit of help from prople with experience in SLSQP, either as advice on what to study more for better understanding, any link to useful knowledge, a comment on the relevant equations from D. Kraft papers or just some explanation.

Thank you in advance.

The papers of D.Kraft attached.