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 x=x0.

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 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.
• The constraints cons can be any logical combination of:
•  lhs==rhs equations lhs>rhs or lhs>=rhs inequalities {x,y,…}∈reg region specification
• 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 x0 and x1 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 xmin to xmax.
• 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.

Examples

open allclose all

Basic Examples(4)

Find a minimum value of the univariate function:

 In[1]:=
 Out[1]=

Find a minimum value of a multivariate function:

 In[1]:=
 Out[1]=

Find a minimum value of a function subject to constraints:

 In[1]:=
 Out[1]=

Find a minimum value of a function over a geometric region:

 In[1]:=
 Out[1]=

See Also

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