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I have been using FindMinimum to find a local minimum of a non-linear function within a constrained region.

How can I know which method Mathematica has selected to find the local minimum?

Thanks in advance!

Excerpt from Some Notes on Internal Implementation of Mathematica:

• With Method->Automatic and two starting values, FindMinimum uses
  Brent's principal axis method. With one starting value for each
  variable, FindMinimum uses BFGS quasi-Newton methods, with a limited
  memory variant for large systems.


• If the function to be minimized
  is a sum of squares, FindMinimum uses the Levenberg–Marquardt method
  (Method->"LevenbergMarquardt").


• With constraints, FindMinimum uses
  interior point methods.

Select the Method that produces the SameQ result as Automatic

Select[#, 
 FindMinimum[Abs[x + 1] + Abs[x + 1.01] + Abs[y + 1], x, y, 
 Method -> #] // Quiet & /@ "Gradient", "ConjugateGradient", 
 "InteriorPoint", "QuasiNewton", "Newton", "LinearProgramming", 
 "QuadraticProgramming", "LevenbergMarquardt", #[[2]] == 
 FindMinimum[Abs[x + 1] + Abs[x + 1.01] + Abs[y + 1], x, y, 
 Method -> Automatic] &] // Quiet

(* "QuasiNewton", 0.01, x -> -1.00683, y -> -1. *)