ArgMax

ArgMax[f, x]
gives a position at which f is maximized.

ArgMax[f, {x, y, ...}]
gives a position at which f is maximized.

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

ArgMax[{f, cons}, {x, y, ...}, dom]
gives a position at which f is maximized over the domain dom, typically Reals or Integers.

Details and OptionsDetails and Options

  • ArgMax[..., vars, ...] is effectively equivalent to vars/.Last[Maximize[..., vars, ...].
  • cons can contain equations, inequalities, or logical combinations of these.
  • If f and cons are linear or polynomial, ArgMax will always find a global maximum.
  • ArgMax will return exact results if given exact input.
  • If ArgMax is given an expression containing approximate numbers, it automatically calls NArgMax.
  • If the maximum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMax 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, ArgMax returns .

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Find a maximizer point for a univariate function:

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

Find a maximizer point for a multivariate function:

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

Find a maximizer point for a function subject to constraints:

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

Find a maximizer point as a function of parameters:

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