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2) every local minimum is a global minimum 3) every critical point that is not a global minimum is a saddle point, and Are these not the same thing?
by thomasahle 10y ago
2) every local minimum is a global minimum
3) every critical point that is not a global minimum is a saddle point, and
Are these not the same thing?
- ot 10y agoOnly if the loss function is C^2 (continuous Hessian), otherwise a critical point could be neither an extremal point or a saddle.
- yaacov 10y ago3 excludes critical points from being local maxima while 2 does not, right?
- coherentpony 10y agof(x) = (1 - x^2)^2 This satisfies 2) but not 3). The point x = 0 is a critical point but it is not a global minimum and it is not a saddle point.
- n4r9 10y agoCould 3) be replaced by "there are no local maxima"?