dampedNewton: Damped Newton optimiser

In smoothemplik: Smoothed Empirical Likelihood

Damped Newton optimiser

Description

Damped Newton optimiser

Usage

dampedNewton(
  fn,
  par,
  thresh = 1e-30,
  itermax = 100,
  verbose = FALSE,
  alpha = 0.3,
  beta = 0.8,
  backeps = 0
)

Arguments

fn	A function that returns a list: f, f', f”. If the function takes vector arguments, the dimensions of the list components must be 1, dim X, (dim X) x (dim X). The function must be (must be twice continuously differentiable at x)
par	Numeric vector: starting point.
thresh	A small scalar: stop when Newton decrement squared falls belowe thresh.
itermax	Maximum iterations. Consider optimisation failed if the maximum is reached.
verbose	Logical: if true, prints the tracing infornation (iteration log). This is a translation of Algorithm 9.5 from \insertCiteboyd2004convexsmoothemplik into C++.
alpha	Back-tracking parameter strictly between 0 and 0.5: acceptance of a decrease in function value by alpha*f of the prediction.
beta	Back-tracking parameter strictly between 0 and 1: reduction of the step size until the stopping criterion is met. 0.1 corresponds to a very crude search, 0.8 corresponds to a less crude search.
backeps	Back-tracking threshold: the search can miss by this much. Consider setting it to 1e-10 if backtracking seems to be failing due to round-off.

Value

A list:

References

\insertAllCited

Examples

f1 <- function(x)
  list(fn = x - log(x), gradient = 1 - 1/x, Hessian = matrix(1/x^2, 1, 1))
optim(2, function(x) f1(x)[["fn"]], gr = function(x) f1(x)[["gradient"]], method = "BFGS")
dampedNewton(f1, 2, verbose = TRUE)

# The minimum of f3 should be roughly at -0.57
f3 <- function(x)
  list(fn = sum(exp(x) + 0.5 * x^2), gradient = exp(x) + x, Hessian =  diag(exp(x) + 1))
dampedNewton(f3, seq(0.1, 5, length.out = 11), verbose = TRUE)

smoothemplik documentation built on Aug. 22, 2025, 1:11 a.m.