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The Davidon-Fletcher-Powell (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods are the first quasi-Newton minimization methods developed. These methods differ only in some details; in general, the BFGS approach is more robust.
fletcher_powell(x0, f, g = NULL,
maxiter = 1000, tol = .Machine$double.eps^(2/3))
f
;
if NULL
, a numerical gradient will be calculated.f
at minimum.The basic idea is to generate a sequence of good approximations to the inverse Hessian matrix, in such a way that the approximations are again positive definite.
steep_descent
## Rosenbrock function
fletcher_powell(c(0, 0), rosenbrock)
# $xmin
# [1] 1 1
# $fmin
# [1] 1.774148e-27
# $niter
# [1] 14
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