FindArgMax

FindArgMax[f,x]
gives the position of a local maximum of f.

FindArgMax[f,{x,x0}]
gives the position of a local maximum of f, found by a search starting from the point .

FindArgMax[f,{{x,x0},{y,y0},}]
gives the position of a local maximum of a function of several variables.

FindArgMax[{f,cons},{{x,x0},{y,y0},}]
gives the position of a local maximum subject to the constraints cons.

FindArgMax[{f,cons},{x,y,}]
starts from a point within the region defined by the constraints.

Details and OptionsDetails and Options

  • FindArgMax[,{x,y,}] is effectively equivalent to {x,y,}/.Last[FindMaximum[,{x,y,},].
  • If the starting point for a variable is given as a list, the values of the variable are taken to be lists with the same dimensions.
  • 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
  • FindArgMax first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
  • FindArgMax has attribute HoldAll, and effectively uses Block to localize variables.
  • FindArgMax[f,{x,x0,x1}] searches for a local maximum in f using and as the first two values of x, avoiding the use of derivatives.
  • FindArgMax[f,{x,x0,xmin,xmax}] searches for a local maximum, stopping the search if x ever gets outside the range to .
  • Except when f and cons are both linear, the results found by FindArgMax may correspond only to local, but not global, maxima.
  • By default, all variables are assumed to be real.
  • For linear f and cons, xIntegers can be used to specify that a variable can take on only integer values.
  • FindArgMax takes the same options as FindMaximum.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Find a point at which the univariate function has a maximum:

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Find a point at which the function Sin[x]Sin[2y] has a maximum:

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Find a point at which a function is a maximum 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)