Byrd, Lu, Nocedal and Zhu (1995): generalized Cauchy point of the compact
limited-memory model B = theta I - W M W' (Algorithm CP), direct primal
subspace minimisation over the free variables backtracked into the box, and a
strong-Wolfe line search with maximal step 1. Pairs are kept when
s'y > eps y'y (at most m). Stops when the projected gradient is at most
pgtol or the relative reduction of f is at most factr times machine epsilon,
the conventions of optim(method = "L-BFGS-B").
Usage
LbfgsbMinimize(
f,
x0,
grad = NULL,
lower = NULL,
upper = NULL,
m = 10,
pgtol = 1e-08,
factr = 1e+07,
max_iter = 1000
)
Arguments
- f
Objective.
- x0
Starting point (projected onto the box).
- grad
Gradient function; central differences when NULL.
- lower, upper
Bounds (default unbounded).
- m
Number of correction pairs.
- pgtol, factr
Tolerances.
- max_iter
Iteration cap.
Value
list(x, fun, grad, projected_gradient, n_iter, n_fev, converged,
message).
References
Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. (1995). A limited
memory algorithm for bound constrained optimization. SIAM Journal on
Scientific Computing 16, 1190-1208.
Examples
rb <- function(x) (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2
LbfgsbMinimize(rb, c(-1.2, 1), lower = c(-2, -2), upper = c(0.5, 2))$x
#> [1] 0.50 0.25
