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

• The results found by FindMinimum may correspond only to local, but not global, minima.

• The following options can be given:

AccuracyGoal	Automatic	the accuracy sought
EvaluationMonitor	None	expression to evaluate whenever f is evaluated
Gradient	Automatic	the list of gradient functions {D[f, x], D[f, y], ... }
MaxIterations	100	maximum number of iterations to use
Method	Automatic	method to use
PrecisionGoal	Automatic	the precision sought
StepMonitor	None	expression to evaluate whenever a step is taken
WorkingPrecision	MachinePrecision	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.

• See Section 1.6.5 and Section 3.9.8.

• Implementation notes: see Section A.9.4.

• New in Version 1; modified in 5.

• Advanced Documentation.