# NMinValue

NMinValue[f,x]

gives the minimum value of f with respect to x.

NMinValue[f,{x,y,}]

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

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

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

NMinValue[,xreg]

constrains x to be in the region reg.

# Details and Options

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

# Examples

open allclose all

## Basic Examples(4)

Find the minimum value of a univariate function:

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Find the minimum value of a multivariate function:

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Find the minimum value of a function subject to constraints:

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

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