biggs_exp6: Biggs EXP6 Function

In jlmelville/funconstrain: Functions for Testing Unconstrained Numerical Optimization

Biggs EXP6 Function

Description

Test function 18 from the More', Garbow and Hillstrom paper.

Usage

biggs_exp6(m = 13)

Arguments

m	Number of summand functions in the objective function. Should be equal to or greater than 6.

Details

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

• Dimensions: Number of parameters n = 6, number of summand functions m >= n.

• Minima: f = 5.65565...e-3 if m = 13; not reported in the MGH (1981) paper is (f = 0) at c(1, 10, 1, 5, 4, 3) and c(4, 10, 3, 5, 1, 1) (and probably others) for all m (probably: I stopped testing after m = 1000).

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")}

Biggs, M. C. (1971). Minimization algorithms making use of non-quadratic properties of the objective function. IMA Journal of Applied Mathematics, 8(3), 315-327.

Examples

fun <- biggs_exp6()
# Optimize using the standard starting point
x0 <- fun$x0
res_x0 <- stats::optim(par = x0, fn = fun$fn, gr = fun$gr, method =
"L-BFGS-B")
# Use your own starting point
res <- stats::optim(1:6, fun$fn, fun$gr, method = "L-BFGS-B")

# Use 20 summand functions
fun20 <- biggs_exp6(m = 20)
res <- stats::optim(fun20$x0, fun20$fn, fun20$gr, method = "L-BFGS-B")

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