BUILT-IN MATHEMATICA SYMBOL

# 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, 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:

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Find a minimum value of a multivariate function:

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Find a minimum value of a function subject to constraints:

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