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Which algorithm is used when we do not use the option Method of FindMinimum[] function.

FindMinimum[f,{x,x0}]
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Please, try to use the documentation search or google before posting such elementary questions. Have you at least tried? The information you want can be found in the documentation center

  • 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.

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Indeed when one types "FindMinimum implementation" in the search bar it is the second hit for me. But perhaps they should have added a link to the implementation docs in the main entry. –  Sjoerd C. de Vries Oct 23 '13 at 5:48
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