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NMaximize

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

NMaximize[f, x]

searches for a global maximum of f with respect to x.

NMaximize[f, {x, y, ...}]

global maximum with respect to several variables.

NMaximize[{f, cons}, vars]

global maximum of f subject to the constraints cons.

Notes NMaximize (Protected, not HoldAll) shares NMinimize's methods, options, and constraint/domain handling. Internally maximises by minimising -f, then negates the objective value in the result. Returns {fmax, {x -\> xmax, ...}}.

Examples (6)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (6)

In[1]:= NMinimize[x^4 - 3 x^2 - x, x]
Out[1]= {-3.51391, {x -> 1.30084}}

In[2]:= NMinimize[{x + y, x^2 + y^2 <= 9}, {x, y}]
Out[2]= {-4.24264, {x -> -2.12132, y -> -2.12132}}

In[3]:= NMinimize[{x + 2 y, x^2 + 2 y^2 <= 3, x + y == 2, x >= 1}, {x, y}]
Out[3]= {2.33333, {x -> 1.66667, y -> 0.333333}}

In[4]:= NMinimize[{x + y, x + 2 y >= 3, x >= -2}, {Element[x, Integers], Element[y, Integers]}]
Out[4]= {1.0, {x -> -1, y -> 2}}

In[5]:= NMinimize[{x, x > 2 && x < 1}, x]
Out[5]= {Infinity, {x -> Indeterminate}}

In[6]:= NMaximize[{x + y, x^2 + y^2 <= 1}, {x, y}]
Out[6]= {1.41421, {x -> 0.707107, y -> 0.707107}}

Implementation notes

Attributes: Protected.

References

See also: NMinimize, FindMinimum, Block, HoldAll, Rule, Sqrt, Round, AccuracyGoal