efficient_bfgs: BFGS Implementation for REML Parameter Estimation

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

BFGS Implementation for REML Parameter Estimation

Description

BFGS optimizer designed for REML optimization of correlation parameters. Combines function evaluation and gradient computation into single call to avoid redundant model refitting.

Usage

efficient_bfgs(par, fn, control = list())

Arguments

par	Numeric vector of initial parameter values.
fn	Function returning list(objective, gradient). Must return both objective value and gradient vector matching length(par).
control	List of control parameters: maxit Maximum iterations, default 50 abstol Absolute convergence tolerance, default sqrt(.Machine$double.eps) reltol Relative convergence tolerance, default sqrt(.Machine$double.eps) initial_damp Initial damping factor, default 1 min_damp Minimum damping before termination, default 2^-16 trace Print iteration progress, default FALSE

Details

Implements BFGS, used internally by lgspline() for optimizing correlation parameters via REML when an analytic REML gradient is supplied.

This is more efficient than native BFGS, since gradient and loss can be computed simultaneously, avoiding re-computing components in "fn" and "gr" separately.

Value

List containing:

par

Parameter vector minimizing objective

value

Minimum objective value

counts

Number of iterations

convergence

TRUE if termination occurred before maxit; this reflects the current stopping rule rather than a separate post-hoc convergence check

message

Description of termination status

vcov

Final approximation of inverse-Hessian, useful for inference

Examples

## Minimize Rosenbrock function
fn <- function(x) {
  # Objective
  f <- 100*(x[2] - x[1]^2)^2 + (1-x[1])^2
  # Gradient
  g <- c(-400*x[1]*(x[2] - x[1]^2) - 2*(1-x[1]),
         200*(x[2] - x[1]^2))
  list(f, g)
}
(res <- efficient_bfgs(c(0.5, 2.5), fn))

## Compare to
(res0 <- stats::optim(c(0.5, 2.5), function(x)fn(x)[[1]], hessian = TRUE))
solve(res0$hessian)

lgspline documentation built on May 8, 2026, 5:07 p.m.