FindMinValue

FindMinValue[f, x]
gives the value at a local minimum of f.

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

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

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

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

Details and OptionsDetails and Options

  • FindMinValue[...] is effectively equivalent to First[FindMinimum[...]].
  • 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.
  • FindMinValue first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
  • FindMinValue has attribute HoldAll, and effectively uses Block to localize variables.
  • FindMinValue[f, {x, x0, x1}] searches for a local minimum in f using and as the first two values of x, avoiding the use of derivatives.
  • FindMinValue[f, {x, x0, xmin, xmax}] searches for a local minimum, stopping the search if x ever gets outside the range to .
  • Except when f and cons are both linear, the results found by FindMinValue may correspond only to local, but not global, minima.
  • 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.
  • FindMinValue takes the same options as FindMinimum.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Find a minimum value of the univariate function:

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

Find a minimum value of a multivariate function:

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

Find a minimum value of a function subject to constraints:

In[1]:=
Click for copyable input
Out[1]=
New in 7
New to Mathematica? Find your learning path »
Have a question? Ask support »