BUILT-IN MATHEMATICA SYMBOL

# ArgMin

ArgMin[f, x]
gives a position at which f is minimized.

ArgMin[f, {x, y, ...}]
gives a position at which f is minimized.

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

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

## Details and OptionsDetails and Options

• ArgMin returns a list of the form .
• ArgMin[..., {x, y, ...}, ...] is effectively equivalent to {x, y, ...}/.Last[Minimize[..., {x, y, ...}, ...].
• cons can contain equations, inequalities or logical combinations of these.
• If f and cons are linear or polynomial, ArgMin will always find a global minimum.
• ArgMin will return exact results if given exact input.
• If ArgMin is given an expression containing approximate numbers, it automatically calls NArgMin.
• If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMin 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, ArgMin returns {Indeterminate, Indeterminate, ...}.

## ExamplesExamplesopen allclose all

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

Find a minimizer point for a univariate function:

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Find a minimizer point for a multivariate function:

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Find a minimizer point for a function subject to constraints:

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Find a minimizer point as a function of parameters:

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