ArgMin

ArgMin[f,x]

gives a position xmin at which f is minimized.

ArgMin[f,{x,y,}]

gives a position {xmin,ymin,} 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 Options  • ArgMin returns a list of the form {xmin,ymin,}.
• 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==rhs equations lhs!=rhs inequations lhs>rhs or lhs>=rhs inequalities {x,y,…}∈reg region 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 xreg, 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 .
• N[ArgMin[]] calls NArgMin for optimization problems that cannot be solved symbolically.

Examples

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Basic Examples(5)

Find a minimizer point for a univariate function:

 In:= Out= Find a minimizer point for a multivariate function:

 In:= Out= Find a minimizer point for a function subject to constraints:

 In:= Out= Find a minimizer point as a function of parameters:

 In:= Out= Find a minimizer point over a geometric region:

 In:= Out= Plot it:

 In:= Out= Possible Issues(2)

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