FindMaxValue

FindMaxValue[f,x]
gives the value at a local maximum of f.

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

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

FindMaxValue[{f,cons},{{x,x0},{y,y0},}]
gives the value at a local maximum subject to the constraints cons.

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

Details and OptionsDetails and Options

  • FindMaxValue[] is effectively equivalent to First[FindMaximum[]].
  • 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
  • FindMaxValue first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
  • FindMaxValue has attribute HoldAll, and effectively uses Block to localize variables.
  • FindMaxValue[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.
  • FindMaxValue[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 FindMaxValue 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.
  • FindMaxValue takes the same options as FindMaximum.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Find a maximum value of a univariate function:

In[1]:=
Click for copyable input
Out[1]=

Find a maximum value of a multivariate function:

In[1]:=
Click for copyable input
Out[1]=

Find a maximum value of a function subject to constraints:

In[1]:=
Click for copyable input
Out[1]=

Find a maximum value of a function in a geometric region:

In[1]:=
Click for copyable input
Out[1]=
Introduced in 2008
(7.0)
| Updated in 2014
(10.0)