helical | R Documentation |
Test function 7 from the More', Garbow and Hillstrom paper.
helical()
The objective function is the sum of m
functions, each of n
parameters.
Dimensions: Number of parameters n = 3
, number of summand
functions m = 3
.
Minima: f = 0
at (1, 0, 0)
.
A list containing:
fn
Objective function which calculates the value given input
parameter vector.
gr
Gradient function which calculates the gradient vector
given input parameter vector.
he
If available, the hessian matrix (second derivatives)
of the function w.r.t. the parameters at the given values.
fg
A function which, given the parameter vector, calculates
both the objective value and gradient, returning a list with members
fn
and gr
, respectively.
x0
Standard starting point.
fmin
reported minimum
xmin
parameters at reported minimum
More', J. J., Garbow, B. S., & Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software (TOMS), 7(1), 17-41. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi.org/10.1145/355934.355936")}
Fletcher, R., & Powell, M. J. (1963). A rapidly convergent descent method for minimization. The Computer Journal, 6(2), 163-168.
fun <- helical()
# Optimize using the standard starting point
x0 <- fun$x0
res_x0 <- stats::optim(par = x0, fn = fun$fn, gr = fun$gr, method =
"L-BFGS-B")
# Use your own starting point
res <- stats::optim(c(0.1, 0.2, 0.3), fun$fn, fun$gr, method = "L-BFGS-B")
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