# 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

open allclose all

## Basic Examples(5)

Find the maximum value of a univariate function:

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Find the maximum value of a multivariate function:

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Find the maximum value of a function subject to constraints:

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

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

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