NArgMax

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

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

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

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

Details and OptionsDetails and Options

  • NArgMax returns a list of the form .
  • NArgMax[,{x,y,}] is effectively equivalent to {x,y,}/.Last[NMaximize[,{x,y,},].
  • 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
  • NArgMax[{f,cons},xreg] is effectively equivalent to NArgMax[{f,consxreg},x].
  • For , the different coordinates can be referred to using Indexed[x,i].
  • NArgMax always attempts to find a global maximum 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, NArgMax can always find global maxima, over both real and integer values.
  • Otherwise, NArgMax may sometimes find only a local maximum.
  • If NArgMax determines that the constraints cannot be satisfied, it returns {Indeterminate,}.
  • NArgMax takes the same options as NMaximize.

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 for a function over a geometric region:

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Plot it:

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