bard: Bard Function

In jlmelville/funconstrain: Functions for Testing Unconstrained Numerical Optimization

Bard Function

Description

Test function 8 from the More', Garbow and Hillstrom paper.

Usage

bard()

Details

The objective function is the sum of m functions, each of n parameters.

• Dimensions: Number of parameters n = 3, number of summand functions m = 15.

• Minima: f = 8.214877e-3 at c(0.08241056, 1.133036, 2.343695) Solvers terminate with f near 17 for parameter 1 in 0.84 to 0.89 approximately and large negative values of the other two parameters.

Value

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

References

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")}

Bard, Y. (1970). Comparison of gradient methods for the solution of nonlinear parameter estimation problems. SIAM Journal on Numerical Analysis, 7(1), 157-186. \Sexpr[results=rd]{tools:::Rd_expr_doi("dx.doi.org/10.1137/0707011")}

Examples

fun <- bard()
# 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")

jlmelville/funconstrain documentation built on April 17, 2024, 7:47 p.m.