fntl (version 0.1.1)

multivariate-optimization: Multivariate Optimization

Description

Multivariate Optimization

Usage

cg1(init, f, g, args)
cg2(init, f, args)
bfgs1(init, f, g, args)
bfgs2(init, f, args)
lbfgsb1(init, f, g, args)
lbfgsb2(init, f, args)
neldermead(init, f, args)
nlm1(init, f, g, h, args)
nlm2(init, f, g, args)
nlm3(init, f, args)

Value

A list with results corresponding to the specified function. See the package vignette for further details.

• cg1 and cg2 return a cg_result which is documented in the section "Conjugate Gradient".

• bfgs1 and bfgs2 return a bfgs_result which is documented in the section "BFGS".

• lbfgsb1 and lbfgsb2 return a lbfgsb_result which is documented in the section "L-BFGS-B".

• neldermead returns a neldermead_result which is documented in the section "Nelder-Mead".

• nlm1, nlm2, and nlm3 return a nlm_result which is documented in the section "Newton-Type Algorithm for Nonlinear Optimization".

Arguments

init

Initial value

f

Function \(f\) to optimize

g

Gradient function of \(f\).

args

List of additional arguments for optimization.

h

Hessian function of \(f\).

Details

The argument args should be a list constructed from one of the following functions:

• bfgs_args for BFGS;

• lbfgsb_args for L-BFGS-B;

• cg_args for CG;

• neldermead_args for Nelder-Mead;

• nlm_args for the Newton-type algorithm used in nlm.

When g or h are omitted, the gradient or Hessian will be respectively be computed via finite differences.

Examples

f = function(x) { sum(x^2) }
g = function(x) { 2*x }
h = function(x) { 2*diag(length(x)) }
x0 = c(1,1)

args = cg_args()
cg1(x0, f, g, args)
cg2(x0, f, args)

args = bfgs_args()
bfgs1(x0, f, g, args)
bfgs2(x0, f, args)

args = lbfgsb_args()
lbfgsb1(x0, f, g, args)
lbfgsb2(x0, f, args)

args = neldermead_args()
neldermead(x0, f, args)

args = nlm_args()
nlm1(x0, f, g, h, args)
nlm2(x0, f, g, args)
nlm3(x0, f, args)