MinValue

MinValue[f, x]
gives the minimum value of f with respect to x.

MinValue[f, {x, y, ...}]
gives the minimum value of f with respect to x, y, ....

MinValue[{f, cons}, {x, y, ...}]
gives the minimum value of f subject to the constraints cons.

MinValue[{f, cons}, {x, y, ...}, dom]
gives the minimum value of f over the domain dom, typically Reals or Integers.

Details and OptionsDetails and Options

  • MinValue[...] is effectively equivalent to First[Minimize[...]].
  • MinValue gives the infimum of values of f. It may not be attained for any values of x, y, ....
  • cons can contain equations, inequalities or logical combinations of these.
  • If f and cons are linear or polynomial, MinValue will always find a global minimum.
  • MinValue will return exact results if given exact input.
  • If MinValue is given an expression containing approximate numbers, it automatically calls NMinValue.
  • If no domain is specified, all variables are assumed to be real.
  • xIntegers can be used to specify that a particular variable can take on only integer values.
  • If the constraints cannot be satisfied, MinValue returns Infinity.

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Find the minimum value of a univariate function:

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Find the minimum value of a multivariate function:

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Find the minimum value of a function subject to constraints:

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Find the minimum value as a function of parameters:

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