BUILT-IN MATHEMATICA SYMBOL

# Maximize

Maximize[f, x]
maximizes f with respect to x.

Maximize[f, {x, y, ...}]
maximizes f with respect to x, y, ....

Maximize[{f, cons}, {x, y, ...}]
maximizes f subject to the constraints cons.

Maximize[{f, cons}, {x, y, ...}, dom]
maximizes with variables over the domain dom, typically Reals or Integers.

## Details and OptionsDetails and Options

• Maximize returns a list of the form .
• cons can contain equations, inequalities, or logical combinations of these.
• If f and cons are linear or polynomial, Maximize will always find a global maximum.
• Maximize will return exact results if given exact input.
• If Maximize is given an expression containing approximate numbers, it automatically calls NMaximize.
• If the maximum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, Maximize will return the supremum and the closest specifiable point.
• If no domain is specified, all variables are assumed to be real.
• can be used to specify that a particular variable can take on only integer values.
• If the constraints cannot be satisfied, Maximize returns {-Infinity, {x->Indeterminate, ...}}.
• Maximize[f, x, WorkingPrecision->n] uses n digits of precision while computing a result. »

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Maximize a univariate function:

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Maximize a multivariate function:

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Maximize a function subject to constraints:

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A maximization problem containing parameters:

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