NArgMax

gives a position x_max at which f is numerically maximized.

NArgMax[f,{x,y,…}]

gives a position {x_max,y_max,…} 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[…,x∈reg]

constrains x to be in the region reg.

Details and Options

NArgMax returns a list of the form {x_min,y_min,…}.
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},x∈reg] is effectively equivalent to NArgMax[{f,cons∧x∈reg},x].
For x∈reg, 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.
x∈Integers 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.