L-BFGS optimizer (limited memory BFGS)

Memory-efficient variant of BFGS that stores only the last m correction pairs instead of the full inverse Hessian approximation. Suitable for large-scale optimization.

Usage

lbfgs(
  objective_fn,
  params,
  m = 10,
  max_iter = 1000,
  tol = 1e-06,
  maximize = FALSE,
  verbose = 0
)

Arguments

objective_fn: Function taking list of value parameters, returns scalar
params: List of value objects (initial parameter values)
m: Number of correction pairs to store, default 10
max_iter: Maximum iterations, default 1000
tol: Convergence tolerance on gradient norm, default 1e-6
maximize: If TRUE, maximize; if FALSE (default), minimize
verbose: Print progress every N iterations (0 for silent)

Value

A list containing:

params: List of value objects at optimum
value: Objective function value at optimum
gradient: Gradient at optimum
iterations: Number of iterations performed
converged: TRUE if gradient norm < tol

Details

L-BFGS uses the two-loop recursion algorithm to compute the search direction without explicitly forming the inverse Hessian. Memory usage is O(m*n) instead of O(n^2) for full BFGS.