Newton's method in optimization

min f(x), x∈Rn


This is the Newton's method in optimization in nonlinear equations.

g(x)=0

x0 is the starting point.


∇g(x0) is linear and non-singular.


x1=x0+d

∴

Therefore, g(x0+d) is almost Zero.

f(x) is the approximation, and T is Taylor expansion.




This is almost g(x0+d). g is the Jacobian matrix, and ∂ is general topology.









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