Is there anyways to know what algorithms mathematica is using to solve optimization problems in Minimize[] or Maximize[] ? because if I use performance as retrieved by Timing[], on a paper I should write what methods has been used to solve the problem. Currently with the help of documentation I can only make guess. However Mathematica should expose what methods it is using to solve in different stages.
Because the topic of optimization is very broad, can you make more specific statement about the exact type of problem with your thesis?
The generic scheme may be found here.
There is a tutorial with a lengthy explanation of methods used in Solve.
tutorial/ComplexPolynomialSystems
If possible, you could use FindMinimum and FindMaximum and specify the method directly: “ConjugateGradient”, “PrincipalAxis”, “LevenbergMarquardt”, “Newton”, “QuasiNewton”, “InteriorPoint”, or “LinearProgramming”. I’m aware that this functions is different from Minimize and Maximize, but sometimes they can be used interchangeably…
When you use Minimize and Maximize, you need to make sure all the numbers in the problem are integers or rationals. Otherwise, NMinimize or NMaximize will be used.