# 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[,xreg]

constrains x to be in the region reg.

# Details and Options • 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.
• The constraints cons can be any logical combination of:
•  lhs==rhs equations lhs>rhs or lhs>=rhs inequalities {x,y,…}∈reg region specification
• NArgMax[{f,cons},xreg] is effectively equivalent to NArgMax[{f,consxreg},x].
• For xreg, the different coordinates can be referred to using Indexed[x,i].
• NArgMax always attempts to find a global maximum 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, NArgMax can always find global maxima, over both real and integer values.
• Otherwise, NArgMax may sometimes find only a local maximum.
• If NArgMax determines that the constraints cannot be satisfied, it returns {Indeterminate,}.
• NArgMax takes the same options as NMaximize.

# Examples

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## Basic Examples(4)

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 function over a geometric region:

Plot it:

## Scope(9)

Or constraints can be specified:

Use NArgMax for linear objective and constraints:

Integer constraints can be imposed:

Maximize over a region:

Plot it:

Find points in two regions realizing the maximum distance:

Plot it:

Find the maximum such that the rectangle and ellipse still intersect:

Plot it:

Find the maximum for which contains the given three points:

Plot it:

Use to specify that is a vector in :

Find points in two regions realizing the maximum distance:

Plot it:

## Applications(1)

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

## Properties & Relations(1)

NMaximize gives both the value of the maximum and the maximizer point:

NArgMax gives the maximizer point:

NMaxValue gives the maximum:

## 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)