shor: Shor's R Algorithm

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

Description

Shor's R algorithm for unconstrained minimization of smooth and non smooth functions.

Usage

shor(fn, gr,nvar = 0, nstart = 10, x0 = NULL,upper = 1, lower = 0, 
    maxit = 1000, fvalquit = -Inf, beta = 0.5, normtol = 1e-06, xnormquit = Inf,
    evaldist = 1e-04, ngrad = 0, rescale = 0,
    strongwolfe = 0, useprevstep = 0, wolfe1 = 1e-04,
    wolfe2 = 0.5, quitLSfail = TRUE, prtlevel = 1)

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).
nvar	Number of parameters that fn() takes.
nstart	Number of initial guesses. Default is 10.
x0	Matrix, with dimension (nvar x nstart), each column represent an initial guess.
upper	upper bound for the initial value
lower	lower bound for the initial value
maxit	maximum number of iterations.
fvalquit	quit if f drops below this value.
beta	the key parameter, between 0 and 1, or nan to minimize the error in the secant equation each iteration (default 1/2) beta = 1: steepest descent; beta -> 0: conjugate gradient (beta = 0 will give divide by 0) note: beta = 1 - gamma, where gamma is notation in IMAJNA paper
normtol	termination tolerance on d: smallest vector in convex hull of up to ngrad gradients (default: 1e-6)
xnormquit	quit if norm(x) drops below this.
evaldist	the gradients used in the termination test qualify only if they are evaluated at points approximately within distance options.evaldist of x
ngrad	number of gradients willing to save and use in solving QP to check optimality tolerance on smallest vector in their convex hull; see also next two options
rescale	1 if rescale B to have inf norm 1 every iteration
strongwolfe	if this is 1, strong line search is used, otherwise, weak line search is used. Default is 0.
useprevstep	if 1, line search is initialized with previous steps. 1 seemed to perform better, but hard to justify this rationally.
wolfe1	wolfe line search parameter 1.
wolfe2	wolfe line search parameter 2.
quitLSfail	1 if want to quit when line search fails. 0 otherwise.
prtlevel	if 1, prints in code messages.

Value

Returns a list containing the following fields:

x	a matrix with k'th column containing final value of x obtained from k'th column of x0.
f	a vector of final obtained minimum values of fn() at the initial points.
g	each column is the gradient at the corresponding column of x
B	list of the final shor matrices
frec	record of function evaluations
betarec	record of beta
xrec	record of iterates
svrec	record of singular value's of the Hessian

Author(s)

Copyright (c) 2010 Michael Overton for Matlab code and documentation, with permission converted to R by Abhirup Mallik (and Hans W Borchers).

See Also

hanso, gradsamp, nlcg, bfgs

Examples

nesterov_f <- function(x) {
    x1 <- x[1]; x2 <- x[2]
    1/4*(x1-1)^2 + abs(x2 - 2*x1^2+1)
 }

nesterov_g <- function(x) {     # analytical gradient
    g <- matrix(NA, 2, 1)
    x1 <- x[1]; x2 <- x[2]
    sgn <- sign(x2 - 2*x1^2 + 1)
    if (sgn != 0) {
        g[1] <- 0.5*(x1-1) - sgn*4*x1
        g[2] <- sgn
    }
    g
 }

rHanso documentation built on May 2, 2019, 5:26 p.m.