NMinimize

Usage

• NMinimize[f, {x, y, ... }] minimizes f numerically with respect to x, y, ... .
• NMinimize[{f, cons}, {x, y, ... }] minimizes f numerically subject to the constraints cons.

Notes

• NMinimize returns a list of the form {

, {x ->

, y ->

, ... }}.

• cons can contain equations, inequalities or logical combinations of these.

• NMinimize always attempts to find a global minimum of f subject to the constraints given.

• Unless f and cons are both linear, NMinimize may sometimes find only a local minimum.

• By default, all variables are assumed to be real.

• x

Integers can be used to specify that a variable can take on only integer values.

• If NMinimize determines that the constraints cannot be satisfied, it returns {Infinity, {x -> Indeterminate, ... }}.

• The following options can be given:

AccuracyGoal	Automatic	the accuracy sought
EvaluationMonitor	None	expression to evaluation whenever f is evaluated
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 maximum, and the value of the function at the minimum.

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

• Possible settings for the Method option include "NelderMead", "DifferentialEvolution", "SimulatedAnnealing" and "RandomSearch".

• See Section 1.6.5 and Section 3.9.8.

• Advanced Documentation.

• Implementation notes: see Section A.9.4.

• See also: NMaximize, Minimize, FindMinimum, FindFit.

• New in Version 5.