[x, options, flog, pointlog] = conjgrad(f, x, options, gradf) uses a
conjugate gradients
algorithm to find the minimum of the function f(x) whose
gradient is given by gradf(x). Here x is a row vector
and f returns a scalar value.
The point at which f has a local minimum
is returned as x. The function value at that point is returned
in options(8). A log of the function values
after each cycle is (optionally) returned in flog, and a log
of the points visited is (optionally) returned in pointlog.
conjgrad(f, x, options, gradf, p1, p2, ...) allows
additional arguments to be passed to f() and gradf().
The optional parameters have the following interpretations.
options(1) is set to 1 to display error values; also logs error
values in the return argument errlog, and the points visited
in the return argument pointslog. If options(1) is set to 0,
then only warning messages are displayed. If options(1) is -1,
then nothing is displayed.
options(2) is a measure of the absolute precision required for the value
of x at the solution. If the absolute difference between
the values of x between two successive steps is less than
options(2), then this condition is satisfied.
options(3) is a measure of the precision required of the objective
function at the solution. If the absolute difference between the
objective function values between two successive steps is less than
options(3), then this condition is satisfied.
Both this and the previous condition must be
satisfied for termination.
options(9) is set to 1 to check the user defined gradient function.
options(10) returns the total number of function evaluations (including
those in any line searches).
options(11) returns the total number of gradient evaluations.
options(14) is the maximum number of iterations; default 100.
options(15) is the precision in parameter space of the line search;
default 1e-4.
w = quasinew('neterr', w, options, 'netgrad', net, x, t);
di that are conjugate: i.e. di*H*d(i-1) = 0,
where H is the Hessian matrix. This means that minimising along
di does not undo the effect of minimising along the previous
direction. The Polak-Ribiere formula is used to calculate new search
directions. The Hessian is not calculated, so there is only an
O(W) storage requirement (where W is the number of
parameters). However, relatively accurate line searches must be used
(default is 1e-04).
graddesc, linemin, minbrack, quasinew, scgCopyright (c) Ian T Nabney (1996-9)