FindMinimum

FindMinimum[f, x, ] searches for a local minimum in f, starting from the point x=.

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.

FindMinimum[f, x, , ] searches for a local minimum in f using and as the first two values of x. This form must be used if symbolic derivatives of f cannot be found.

FindMinimum[f, x, xstart, xmin, xmax] searches for a local minimum, stopping the search if x ever gets outside the range xmin to xmax.

FindMinimum[f, x, , y, , ... ] searches for a local minimum in a function of several variables.

FindMinimum has attribute HoldAll.

FindMinimum works by following the path of steepest descent from each point that it reaches. The minima it finds are local, but not necessarily global, ones.

The following options can be given:

The default settings for AccuracyGoal and PrecisionGoal are 10 digits less than WorkingPrecision.

FindMinimum continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved.

A Method option can also be given. Possible settings include Gradient, LevenbergMarquardt, Newton and QuasiNewton, with the default being Automatic.

See The Mathematica Book: Section 1.6.5 and Section 3.9.8.

Implementation Notes: see section A.9.4.

See also: ConstrainedMin, LinearProgramming, D, Fit.

Related package: Statistics`NonlinearFit`.

Further Examples