kow_osb: Kowalik and Osborne Function

In jlmelville/funconstrain: Functions for Testing Unconstrained Numerical Optimization

Kowalik and Osborne Function

Description

Test function 15 from the More', Garbow and Hillstrom paper.

Usage

kow_osb()

Details

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

• Dimensions: Number of parameters n = 4, number of summand functions m = 11.

• Minima: f = 3.07505...e-4; and f = 1.02734...e-3 at (Inf, -14.07..., -Inf, -Inf).

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")}

Kowalik, J. S., & Osborne, M. R. (1968). Methods for unconstrained optimization problems. New York, NY: Elsevier North-Holland.

Examples

fun <- kow_osb()
# Optimize using the standard starting point
x0 <- fun$x0
res_x0 <- stats::optim(par = x0, fn = fun$fn, gr = fun$gr, method =
"L-BFGS-B")
# Use your own starting point
res <- stats::optim(c(0.1, 0.2, 0.3, 0.4), fun$fn, fun$gr, method =
"L-BFGS-B")

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