# FindMinimum

Usage

FindMinimum[f, {x, }] searches for a local minimum in f, starting from the point x=.
FindMinimum[f, {{x, }, {y, }, ... }] searches for a local minimum in a function of several variables.

Notes

FindMinimum returns a list of the form {, {x->}}, where is the minimum value of f found, and is the value of x for which it is found.
• If the starting point for a variable is given as a list, the values of the variable are taken to be lists with the same dimensions.
FindMinimum has attribute HoldAll.
FindMinimum[f, {x, , }] searches for a local minimum in f using and as the first two values of x, avoiding the use of derivatives.
FindMinimum[f, {x, , , }] searches for a local minimum, stopping the search if x ever gets outside the range to .
• The results found by FindMinimum may correspond only to local, but not global, minima.
• The following options can be given:
 the accuracy sought expression to evaluate whenever f is evaluated Gradient the list of gradient functions {D[f, x], D[f, y], ... } MaxIterations 100 maximum number of iterations to use Method method to use the precision sought expression to evaluate whenever a step is taken the precision used in internal computations
• The default settings for AccuracyGoal and PrecisionGoal are WorkingPrecision/2.
• The settings for AccuracyGoal and PrecisionGoal specify the number of digits to seek in both the value of the position of the minimum, and the value of the function at the minimum.
FindMinimum continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved.
• Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton" and "QuasiNewton", with the default being Automatic.
• Implementation notes: see Section A.9.4.
• New in Version 1; modified in 5.