BUILT-IN MATHEMATICA SYMBOL

# ArgMax

ArgMax[f, x]
gives a position at which f is maximized.

ArgMax[f, {x, y, ...}]
gives a position at which f is maximized.

ArgMax[{f, cons}, {x, y, ...}]
gives a position at which f is maximized subject to the constraints cons.

ArgMax[{f, cons}, {x, y, ...}, dom]
gives a position at which f is maximized over the domain dom, typically Reals or Integers.

## Details and OptionsDetails and Options

• ArgMax[..., vars, ...] is effectively equivalent to vars/.Last[Maximize[..., vars, ...].
• cons can contain equations, inequalities, or logical combinations of these.
• If f and cons are linear or polynomial, ArgMax will always find a global maximum.
• ArgMax will return exact results if given exact input.
• If ArgMax is given an expression containing approximate numbers, it automatically calls NArgMax.
• If the maximum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMax will return 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, ArgMax returns .

## ExamplesExamplesopen allclose all

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

Find a maximizer point for a univariate function:

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Find a maximizer point for a multivariate function:

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Find a maximizer point for a function subject to constraints:

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Find a maximizer point as a function of parameters:

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