NMinValue

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

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

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

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

Details and OptionsDetails and Options

  • NMinValue[] is effectively equivalent to First[NMinimize[]].
  • cons can contain equations, inequalities or logical combinations of these.
  • The constraints cons can be any logical combination of:
  • lhs==rhsequations
    or inequalities
    {x,y,}regregion specification
  • NMinValue[{f,cons},xreg] is effectively equivalent to NMinValue[{f,consxreg},x].
  • For , the different coordinates can be referred to using Indexed[x,i].
  • NMinValue always attempts to find a global minimum of f subject to the constraints given.
  • By default, all variables are assumed to be real.
  • xIntegers can be used to specify that a variable can take on only integer values.
  • If f and cons are linear, NMinValue can always find global minima, over both real and integer values.
  • Otherwise, NMinValue may sometimes find only a local minimum.
  • If NMinValue determines that the constraints cannot be satisfied, it returns Infinity.
  • NMinValue takes the same options as NMinimize.

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 of a function over a geometric region:

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