ArgMin

ArgMin[f,x]
gives a position at which f is minimized.

ArgMin[f,{x,y,}]
gives a position at which f is minimized.

ArgMin[{f,cons},{x,y,}]
gives a position at which f is minimized subject to the constraints cons.

ArgMin[,xreg]
constrains x to be in the region reg.

ArgMin[,,dom]
constrains variables to the domain dom, typically Reals or Integers.

Details and OptionsDetails and Options

  • ArgMin returns a list of the form .
  • ArgMin[,{x,y,},] is effectively equivalent to {x,y,}/.Last[Minimize[,{x,y,},].
  • cons can contain equations, inequalities or logical combinations of these.
  • The constraints cons can be any logical combination of:
  • lhs==rhsequations
    lhs!=rhsinequations
    or inequalities
    {x,y,}regregion specification
    Exists[x,cond,expr]existential quantifiers
  • If f and cons are linear or polynomial, ArgMin will always find a global minimum.
  • ArgMin[{f,cons},xreg] is effectively equivalent to ArgMin[{f,consxreg},x].
  • For , the different coordinates can be referred to using Indexed[x,i].
  • ArgMin will return exact results if given exact input.
  • If ArgMin is given an expression containing approximate numbers, it automatically calls NArgMin.
  • If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMin will return the closest specifiable point.
  • If no domain is specified, all variables are assumed to be real.
  • xIntegers can be used to specify that a particular variable can take on only integer values.
  • If the constraints cannot be satisfied, ArgMin returns {Indeterminate,Indeterminate,}.
  • N[ArgMin[]] calls NArgMin for optimization problems that cannot be solved symbolically.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Find a minimizer point for a univariate function:

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

Find a minimizer point for a multivariate function:

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

Find a minimizer point for a function subject to constraints:

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

Find a minimizer point as a function of parameters:

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

Find a minimizer point over a geometric region:

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

Plot it:

In[2]:=
Click for copyable input
Out[2]=
Introduced in 2008
(7.0)
| Updated in 2014
(10.0)