This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FindArgMax

 FindArgMaxgives the position of a local maximum of f. FindArgMaxgives the position of a local maximum of f, found by a search starting from the point . FindArgMaxgives the position of a local maximum of a function of several variables. FindArgMax gives the position of a local maximum subject to the constraints cons. FindArgMaxstarts from a point within the region defined by the constraints.
• 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.
• FindArgMax first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
• FindArgMax searches for a local maximum in f using and as the first two values of x, avoiding the use of derivatives.
• FindArgMax searches for a local maximum, stopping the search if x ever gets outside the range to .
• Except when f and cons are both linear, the results found by FindArgMax may correspond only to local, but not global, maxima.
• 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.
Find a point at which the univariate function has a maximum:
Find a point at which the function Sin[x]Sin[2y] has a maximum:
Find a point at which a function is a maximum subject to constraints:
Find a point at which the univariate function has a maximum:
 Out[1]=

Find a point at which the function Sin[x]Sin[2y] has a maximum:
 Out[1]=

Find a point at which a function is a maximum subject to constraints:
 Out[1]=
 Scope   (6)
With different starting points, get the locations of different local maxima:
Location of a local maximum of a two-variable function starting from , :
Location of a local maximum constrained within a disk:
Starting point does not have to be provided:
For linear objective and constraints, integer constraints can be imposed:
Or constraints can be specified:
 Options   (7)
This enforces convergence criteria and :
This enforces convergence criteria and :
Setting a high WorkingPrecision makes the process convergent:
Plot convergence to the local maximum:
Use a given gradient; the Hessian is computed automatically: