FindArgMax

FindArgMax[f,x]

gives the position xmax of a local maximum of f.

FindArgMax[f,{x,x0}]

gives the position xmax of a local maximum of f, found by a search starting from the point x=x0.

FindArgMax[f,{{x,x0},{y,y0},}]

gives the position {xmax,ymax,} 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 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==rhs equations lhs>rhs or lhs>=rhs inequalities {x,y,…}∈reg region 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 x0 and x1 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 xmin to xmax.
• 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.

Examples

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Basic Examples(4)

Find a point {x} at which the univariate function -2x^2-3x+5 has a maximum:

 In:= Out= Find a point {x,y} at which the function Sin[x]Sin[2y] has a maximum:

 In:= Out= Find a point at which a function is a maximum subject to constraints:

 In:= Out= Find a maximizer point for a function over a geometric region:

 In:= Out= Plot it:

 In:= Out= Possible Issues(4)

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