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NArgMax

NArgMax[f, x]
gives a position xmax at which f is numerically maximized.
NArgMax[f, {x, y, ...}]
gives a position {xmax, ymax, ...} at which f is numerically maximized.
NArgMax[{f, cons}, {x, y, ...}]
gives a position at which f is numerically maximized subject to the constraints cons.
  • NArgMax returns a list of the form {xmin, ymin, ...}.
  • NArgMax[..., {x, y, ...}] is effectively equivalent to {x, y, ...}/.Last[NMaximize[..., {x, y, ...}, ...].
  • cons can contain equations, inequalities or logical combinations of these.
  • NArgMax always attempts to find a global maximum of f subject to the constraints given.
  • By default, all variables are assumed to be real.
  • xElementIntegers can be used to specify that a variable can take on only integer values.
  • If f and cons are linear, NArgMax can always find global maxima, over both real and integer values.
  • Otherwise, NArgMax may sometimes find only a local maximum.
Find a maximizer point for a univariate function:
Find a maximizer point for a multivariate function:
Find a maximizer point for a function subject to constraints:
Find a maximizer point for a univariate function:
In[1]:=
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Out[1]=
 
Find a maximizer point for a multivariate function:
In[1]:=
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Out[1]=
 
Find a maximizer point for a function subject to constraints:
In[1]:=
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Out[1]=
Find the lengths of sides of a unit perimeter rectangle with the maximal area:
NMaximize gives both the value of the maximum and the maximizer point:
NArgMax gives the maximizer point:
NMaxValue gives the maximum:
The objective function may be unbounded:
There may be no points satisfying the constraints:
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