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NMinimize   (Built-in Mathematica Symbol)
NMinimize[f, x] minimizes f numerically with respect to x.NMinimize[f, {x, y, ...}] minimizes f numerically with respect to x, y, .... NMinimize[{f, cons}, {x, y, ...}] ...
Gauss–Newton Methods   (Mathematica Tutorial)
For minimization problems for which the objective function is a sum of squares, it is often advantageous to use the special structure of the problem. Time and effort can be ...
Variables and Starting Conditions   (Mathematica Tutorial)
All the functions FindMinimum, FindMaximum, and FindRoot take variable specifications of the same form. The function FindFit uses the same form for its parameter ...
Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...
LeastSquares   (Built-in Mathematica Symbol)
LeastSquares[m, b] finds an x that solves the linear least-squares problem for the matrix equation m.x == b.
Fit   (Built-in Mathematica Symbol)
Fit[data, funs, vars] finds a least-squares fit to a list of data as a linear combination of the functions funs of variables vars.
NonlinearModelFit   (Built-in Mathematica Symbol)
NonlinearModelFit[{y_1, y_2, ...}, form, {\[Beta]_1, ...}, x] constructs a nonlinear model with structure form that fits the y_i for successive x values 1, 2, ... using the ...
Principal Axis Method   (Mathematica Tutorial)
"Gauss–Newton" and "conjugate gradient" methods use derivatives. When Mathematica cannot compute symbolic derivatives, finite differences will be used. Computing derivatives ...
Symbolic Evaluation   (Mathematica Tutorial)
The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...
Method   (Built-in Mathematica Symbol)
Method is an option for various algorithm-intensive functions that specifies what internal methods they should use.
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