linesch_sw: strong Wolfe line search

In rnso: An R Implementation of Hybrid Algorithm for Non-Smooth Optimization (HANSO)

Description

strong Wolfe line search with cubic interpolation. Can be used by using strongwolfe=1 in BFGS. For non smooth functions, this is not recommended for BFGS. Use weak line search instead. recommended for use with CG, where strong Wolfe condition needed for convergence analysis

Usage

linesch_sw(fn, gr, x0, d, f0 = fn(x0), grad0 = gr(x0), c1 = 0, c2 = 0.5, fvalquit = -Inf, prtlevel = 0)

Arguments

fn	A function to be minimized. fn(x) takes input as a vector of parameters over which minimization is to take place. fn() returns a scaler.
gr	A function to return the gradient for fn(x).
x0	initial point
d	search direction
f0	fn(x0)
grad0	gr(x0)
c1	Wolfe parameter for the sufficient decrease condition
c2	c2: Wolfe parameter for the WEAK condition on directional derivative
fvalquit	quit if f gets below this value.
prtlevel	prints messages if this is 1

Value

returns a list containing the following fields:

alpha	steplength satisfying Wolfe conditions
x	x0 + alpha*d
f	f(x0 + alpha d)
grad	(grad f)(x0 + alpha d)
fail	0 if both Wolfe conditions satisfied, or falpha < fvalquit 1 if one or both Wolfe conditions not satisfied but an interval was found bracketing a point where both satisfied -1 if no such interval was found, function may be unbounded below
nsteps	number of steps taken in lszoom

Author(s)

Abhirup Mallik, Hans Werner Borchers

References

Numerical Optimization by Jorge Nocedal and Stephen J. Wright

Examples

fr <- function(x) {   ## Rosenbrock Banana function
  x1 <- x[1]
  x2 <- x[2]
  100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
grr <- function(x) { ## Gradient of 'fr'
  x1 <- x[1]
  x2 <- x[2]
  c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1),
    200 *      (x2 - x1 * x1))
}

res=linesch_sw(fr,grr,c(-1.2,1),c(1,1))

rnso documentation built on May 2, 2019, 6:12 p.m.