This function is a direct translation from the Matlab source code of the minimize function from Carl Edward Rasmussen.
minimize(X, f, length, red, dims, data, target, epochSwitch, matMult)Starting point. An Array of the weights.
Function for calculating the function value and the partial derivatives
Maximum number of line searches or maximum allowed number of function evaluations if negative
Expected reduction in function value in the first search.
Parameter to the function f.
Parameter to the function f.
Parameter to the function f.
Parameter to the function f.
Matrix multiplication function.
The function returns the found solution "X", a vector of function values "fX" indicating the progress made and "i" the number of iterations (line searches or function evaluations, depending on the sign of "length") used.
Minimize a differentiable multivariate function.
Usage: [X, fX, i] <- minimize(X, f, length, P1, P2, P3, ... )
where the starting point is given by "X" (D by 1), and the function named in the string "f", must return a function value and a vector of partial derivatives of f wrt X, the "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. You can (optionally) give "length" a second component, which will indicate the reduction in function value to be expected in the first line-search (defaults to 1.0). The parameters P1, P2, P3, ... are passed on to the function f.
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 (i.e., there may be a bug in the implementation of your "f" function). The function returns the found solution "X", a vector of function values "fX" indicating the progress made and "i" the number of iterations (line searches or function evaluations, depending on the sign of "length") used. 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. See also: checkgrad Copyright (C) 2001 - 2006 by Carl Edward Rasmussen (2006-09-08).