linfun_r1z: Linear Function - Rank 1 with Zero Columns and Rows

In jlmelville/funconstrain: Functions for Testing Unconstrained Numerical Optimization

Linear Function - Rank 1 with Zero Columns and Rows

Description

Test function 34 from the More', Garbow and Hillstrom paper.

Usage

linfun_r1z(m = 100)

Arguments

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

Details

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

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

• Minima: f = (m * m + 3 * m - 6) / (2 * (2 * m - 3)) at any set of points x[j] with j = 2, ..., n - 1 where the sum of j * x[j] = 3 / (2 * m - 3).

The number of parameters, n, in the objective function is not specified when invoking this function. It is implicitly set by the length of the parameter vector passed to the objective and gradient functions that this function creates. See the 'Examples' section.

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 Function returning the standard starting point, given n, the number of variables desired.

• 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")}

Examples

linr1z <- linfun_r1z(m = 10)
# 6 variable problem using the standard starting point
x0_6 <- linr1z$x0(n = 6)
res_6 <- stats::optim(x0_6, linr1z$fn, linr1z$gr, method = "L-BFGS-B")
# Standing starting point with 8 variables
res_8 <- stats::optim(linr1z$x0(8), linr1z$fn, linr1z$gr, method =
"L-BFGS-B")
# Create your own 4 variable starting point
res_4 <- stats::optim(c(0.1, 0.2, 0.3, 0.4), linr1z$fn, linr1z$gr,
                      method = "L-BFGS-B")
# Use 20 summand functions
linr1z_m20 <- linfun_r1z(m = 20)
# Repeat 4 parameter optimization with new test function
res_n4_m20 <- stats::optim(c(0.1, 0.2, 0.3, 0.4), linr1z_m20$fn,
linr1z_m20$gr, method = "L-BFGS-B")

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