Gekko Python3. System of equations

Question

I would like to know that is the theoretical method that is behind the APM SOLVERs.

I am solving a problem where I have to solve a system of non-linear equations without any kind of constraints. I am using BPOPT solver and it works fine. I just would like to know what method is being used to solve such systems. It is Newton's method? Quasi-Newtons's method? I don't find any documentation about this. Could you please tell me where I can find such information?

Is it also possible to know a priori the RAM that gekko solver will need to solve a system of non-linear equations with (N) variables?

Thank you

Answer 1

There is additional information on the APOPT Solver:

• 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. Presentation
• Wikipedia Article on APOPT
• apopt.com web-site
• APMonitor Solver documentation

The BPOPT and IPOPT solvers are interior point methods while the APOPT solver is a Mixed Integer Nonlinear Programming (NLP) solver that uses an active-set SQP solver with branch and bound for integer variables.

It is difficult to know a priori the amount of memory that will be used. You may be able to monitor the local apm solve process with a tool such as psutil as discussed in How to get current CPU and RAM usage in Python? There is also more information on solver methods in the design optimization course and online textbook on optimization.