ISOpure.model_optimize.cg_code.rminimize {ISOpureR}

Minimize a differentiable multivariate function

Description

This function is a conjugate-gradient search with interpolation/extrapolation by Carl Edward Rasmussen. A description of the Matlab code can be found at http://learning.eng.cam.ac.uk/carl/code/minimize/ (accessed Jan. 21, 2014). This is a implementation in R.

Usage

ISOpure.model_optimize.cg_code.rminimize(X, f, df, run_length, ...)

Arguments

X

The starting point is given by X which must be either a scalar or a column vector or matrix, not a row matrix

f

The name of the function to be minimized, returning a scalar

df

The name of the function which returns the vector of partial derivatives of f wrt X, where again the partial derivatives must be in scalar or column vector/matrix form

run_length

Gives the length of the run: if it is positive, it gives the maximum number of line searches, if negative its absolute gives the maximum allowed number of function evaluations. Note, for ISOpureR, used only positive run_length.

...

Parameters to be passed on to the function f.

Details

The function returns when either its length is up, or if no further progress can be made (ie, we are at a (local) minimum, or so close that due to numerical problems, we cannot get any closer). NOTE: If the function terminates within a few iterations, it could be an indication that the function values and derivatives are not consistent (ie, there may be a bug in the implementation of your "f" function).

The Polack-Ribiere flavour of conjugate gradients is used to compute search directions, and a line search using quadratic and cubic polynomial approximations and the Wolfe-Powell stopping criteria is used together with the slope ratio method for guessing initial step sizes. Additionally a bunch of checks are made to make sure that exploration is taking place and that extrapolation will not be unboundedly large.

Value

A list with three components:

X

The found solution X

fX

A vector of function values fX indicating the progress made

i

The number of iterations

Author(s)

Catalina Anghel, Francis Nguyen, Carl Edward Rasmussen

Examples

# Example from Carl E. Rasmussen's webpage

rosenbrock <- function(x){
	D <- length(x);
 	y <- sum(100*(x[2:D] - x[1:(D-1)]^2)^2 + (1-x[1:(D-1)])^2);
 	return(y);
 	};
drosenbrock <- function(x){
	D <- length(x);
	df <- numeric(D);
	df[1:D-1] <- -400*x[1:(D-1)]*(x[2:D]-x[1:(D-1)]^2) - 2*(1-x[1:(D-1)]);
  	df[2:D] <- df[2:D] + 200*(x[2:D]-x[1:(D-1)]^2);
  	return(df);
	};

ISOpure.model_optimize.cg_code.rminimize(c(0,0), rosenbrock, drosenbrock, 25)
#
# [[1]]
# [1] 1 1
#
# [[2]]
#  [1] 1.000000e+00 7.716094e-01 5.822402e-01 4.049274e-01 3.246633e-01
#  [6] 2.896041e-01 7.623420e-02 6.786212e-02 3.378424e-02 1.089908e-03
# [11] 1.087952e-03 8.974308e-05 1.218382e-07 6.756019e-09 3.870791e-15
# [16] 1.035408e-21 6.248025e-27 5.719242e-30 4.930381e-32
#
# [[3]]
# [1] 20