Function Repository Resource:

GlobalMinima

Source Notebook

Compute the global minima of an expression with respect to the given variables

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["GlobalMinima"][expr,x]

computes the global minima of expr with respect to x.

ResourceFunction["GlobalMinima"][expr,{x,y,…}]

computes the global minima of expr with respect to multiple variables.

ResourceFunction["GlobalMinima"][{expr,const},{x,y,…}]

computes the global minima of expr subject to the constraint const.

Details and Options

ResourceFunction["GlobalMinima"] returns a list with each minimum in the form {f_min,{x→x_min,y→y_min,…}}.

The const can contain equations, inequalities or logical combinations of these.

ResourceFunction["GlobalMinima"] only returns results when there is a bounded minimum.

Examples

Basic Examples (2)

Compute the global minima of a polynomial:

In[1]:=

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Plot them:

In[2]:=

$Plot[x^2 (x + 2) (x - 2), {x, -3, 3}, Epilog -> { Directive[Red, PointSize[Large]], Point[{-Sqrt[2], -4}], Point[{ Sqrt[2], -4}]}]$

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Scope (2)

Use a constraint in order to reduce the domain upon which minima can be found:

In[3]:=

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Compute the minima of a function of two variables:

In[4]:=

$ResourceFunction["GlobalMinima"][( x^2 + y^2 - 4)^2, {x, y}]$

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Possible Issues (1)

GlobalMinima may return duplicate results for periodic functions:

In[5]:=

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Publisher

Wolfram|Alpha Math Team

Version History

2.0.0 – 23 March 2023
1.0.0 – 18 September 2020

Related Resources

Author Notes

To view the full source code for GlobalMaxima, run the following code: