# NMaxValue

NMaxValue[f,x]

gives the maximum value of f with respect to x.

NMaxValue[f,{x,y,}]

gives the maximum value of f with respect to x, y, .

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

gives the maximum value of f subject to the constraints cons.

NMaxValue[,xreg]

constrains x to be in the region reg.

# Details and Options • NMaxValue[] is effectively equivalent to First[NMaximize[]].
• 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
• NMaxValue[{f,cons},xreg] is effectively equivalent to NMaxValue[{f,consxreg},x].
• For xreg, the different coordinates can be referred to using Indexed[x,i].
• NMaxValue 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, NMaxValue can always find global maxima, over both real and integer values.
• Otherwise, NMaxValue may sometimes find only a local maximum.
• If NMaxValue determines that the constraints cannot be satisfied, it returns .
• NMaxValue takes the same options as NMaximize.

# Examples

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## Basic Examples(5)

Find the maximum value of a univariate function:

Find the maximum value of a multivariate function:

Find the maximum value of a function subject to constraints:

Find the maximum value of a function over a geometric region:

Find the maximum value of a function over a geometric region:

## Scope(9)

Or constraints can be specified:

Use NMaxValue for linear objective and constraints:

Integer constraints can be imposed:

Find the maximum value of a function over a geometric region:

Plot it:

Find the maximum distance between points in two regions:

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

Plot it:

Find the maximum for which contains the given three points:

Use to specify that is a vector in :

Find the maximum distance between points in two regions:

## Applications(1)

Find the maximal area among rectangles with a unit perimeter:

## Properties & Relations(3)

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

NMaxValue gives the maximum:

NArgMax gives the maximizer point:

NMaxValue can solve linear programming problems:

LinearProgramming can be used to solve the same problem given in matrix notation:

Use RegionBounds to compute the bounding box:

Use NMaxValue and NMinValue to compute the same bounds:

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