minimize: Minimize function for differentiable multivariate functions.
In gpr: A Minimalistic package to apply Gaussian Process in R

Description Usage Arguments Value Author(s) References Examples

Performs mimization on a differentiable multivariate function and returns a function value and a vector of partial derivatives the input 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.

Details from gpml: Please consider that minimize execution path computes a new search direction during extrapolation using conjugate gradients (Polack-Ribiere flavour), or reverts to steepest if there was a problem in the previous line-search. Returns the best value so far, if two consecutive line-searches fail, or whenever it run out of function evaluations or line-searches. During extrapolation, the "f" function may fail either with an error or returning Nan or Inf, and minimize should handle this gracefully. If minimize stopped 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).

1	minimize(X, f, .length, covfunc, x, y)

`X`	Starting point is given by array `X` .
`f`	`f` is a string value containing the function name which is supposed to apply minimize on it.
`.length`	`.length` defines how long minimize procedure must be executed.
`covfunc`	is string value that gives the name of covariance function which is passed on to the function `f`.
`x`	Input parameter which is passed on to the function `f`.
`y`	An other input parameter like x which is passed on to the function. It usually defines target value function covfunc and the input array x. `f`.

if .length is positive, it defines the maximum number of line searches, if negative its absolute gives the maximum allowed number of function evaluations. .length can have a second optional component, which indicates the reduction in function value to be expected in the first line-search. its default value is 1.0 .

The function returns when either its length is up, or if no further progress can be made due to a (local) minimum or due to numerical problems. The function returns a list consisting of the found solution X, a vector of function values fX indicating the progress made and i the number of iterations.

Afshin Sadeghi

Carl Edward Rasmussen and Christopher K. I. Williams.Gaussian Processes for Machine Learning. MIT Press, 2006. ISBN 0-262-18253-X. Carl Edward Rasmussen & Hannes Nickisch. gpml(GAUSSIAN PROCESS REGRESSION AND CLASSIFICATION Toolbox) Matlab Library.

loghyper= array(c(-1,-1,-1), dim=c(3,1))
covfunc ="covSum,covSEiso,covNoise"
x= array(c(1,1,0,0), dim=c(2,2))
y= array(c(1,0), dim=c(2,1))
loghyper = minimize(loghyper, 'gpr', 10, covfunc, x, y)
loghyper

[[1]]
           [,1]
[1,] -1.0000000
[2,] -2.6177289
[3,] -0.3518741

[[2]]
       [,1]
   2.850202
f0 2.180126
f0 2.147200
f0 2.146995
f0 2.144900
f0 2.144789
f0 2.144787

[[3]]
[1] 9