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[,xreg]
constrains x to be in the region reg.

MinValue[,,dom]
constrains variables to 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.
  • The constraints cons can be any logical combination of:
  • lhs==rhsequations
    lhs!=rhsinequations
    or inequalities
    {x,y,}regregion specification
    Exists[x,cond,expr]existential quantifiers
  • If f and cons are linear or polynomial, MinValue will always find a global minimum.
  • MinValue[{f,cons},xreg] is effectively equivalent to MinValue[{f,consxreg},x].
  • For , the different coordinates can be referred to using Indexed[x,i].
  • 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.
  • N[MinValue[]] calls NMinValue for optimization problems that cannot be solved symbolically.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

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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Find the minimum value of a function over a geometric region:

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Introduced in 2008
(7.0)
| Updated in 2014
(10.0)