# NArgMin

NArgMin[f,x]

gives a position xmin at which f is numerically minimized.

NArgMin[f,{x,y,}]

gives a position {xmin,ymin,} at which f is numerically minimized.

NArgMin[{f,cons},{x,y,}]

gives a position at which f is numerically minimized subject to the constraints cons.

NArgMin[,xreg]

constrains x to be in the region reg.

# Details and Options • NArgMin returns a list of the form {xmin,ymin,}.
• NArgMin[,{x,y,}] is effectively equivalent to {x,y,}/.Last[NMinimize[,{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 or lhs>=rhs inequalities {x,y,…}∈reg region specification
• NArgMin[{f,cons},xreg] is effectively equivalent to NArgMin[{f,consxreg},x].
• For xreg, the different coordinates can be referred to using Indexed[x,i].
• NArgMin always attempts to find a global minimum of f subject to the constraints given.
• By default, all variables are assumed to be real.
• xIntegers can be used to specify that a variable can take on only integer values.
• If f and cons are linear, NArgMin can always find global minima, over both real and integer values.
• Otherwise, NArgMin may sometimes find only a local minimum.
• If NArgMin determines that the constraints cannot be satisfied, it returns {Indeterminate,}.
• NArgMin takes the same options as NMinimize.

# Examples

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## Basic Examples(4)

Find a minimizer point for a univariate function:

Find a minimizer point for a multivariate function:

Find a minimizer point for a function subject to constraints:

Find a minimizer point over a geometric region:

Plot it:

## Scope(9)

Or constraints can be specified:

Use NArgMin for linear objectives and constraints:

Integer constraints can be imposed:

Minimize over a region:

Plot it:

Find the minimum distance between two regions:

Plot it:

Find the minimum such that the triangle and ellipse still intersect:

Plot it:

Find the disk of minimum radius that contains the given three points:

Plot it:

Using Circumsphere gives the same result directly:

Use to specify that is a vector in :

Find the minimum distance between two regions:

Plot it:

## Applications(2)

Find the lengths of sides of a unit area rectangle with minimal perimeter:

Find the lengths of sides of a unit area triangle with minimal perimeter:

## Properties & Relations(2)

NMinimize gives both the value of the minimum and the minimizer point:

NArgMin gives the minimizer point:

NMinValue gives the minimum:

Use RegionNearest to compute a nearest point in the given region:

It can be computed using NArgMin:

## Possible Issues(2)

The objective function may be unbounded: There may be no points satisfying the constraints: Introduced in 2008
(7.0)
|
Updated in 2014
(10.0)