Previous: Solvers, Up: Nonlinear Equations [Contents][Index]
Often it is useful to find the minimum value of a function rather than just
the zeroes where it crosses the x-axis. fminbnd
is designed for the
simpler, but very common, case of a univariate function where the interval
to search is bounded. For unbounded minimization of a function with
potentially many variables use fminunc
or fminsearch
. The two
functions use different internal algorithms and some knowledge of the objective
function is required. For functions which can be differentiated, fminunc
is appropriate. For functions with discontinuities, or for which a gradient
search would fail, use fminsearch
. See Optimization, for
minimization with the presence of constraint functions. Note that searches
can be made for maxima by simply inverting the objective function
(Fto_max = -Fto_min
).
Find a minimum point of a univariate function.
fun should be a function handle or name. a, b specify a
starting interval. options is a structure specifying additional
options. Currently, fminbnd
recognizes these options:
"FunValCheck"
, "OutputFcn"
, "TolX"
,
"MaxIter"
, "MaxFunEvals"
. For a description of these
options, see optimset.
On exit, the function returns x, the approximate minimum point and fval, the function value thereof. info is an exit flag that can have these values:
Notes: The search for a minimum is restricted to be in the interval
bound by a and b. If you only have an initial point
to begin searching from you will need to use an unconstrained
minimization algorithm such as fminunc
or fminsearch
.
fminbnd
internally uses a Golden Section search strategy.
See also: fzero, fminunc, fminsearch, optimset.
Solve an unconstrained optimization problem defined by the function fcn.
fcn should accepts a vector (array) defining the unknown variables,
and return the objective function value, optionally with gradient.
In other words, this function attempts to determine a vector x such
that fcn (x)
is a local minimum.
x0 determines a starting guess. The shape of x0 is preserved
in all calls to fcn, but otherwise is treated as a column vector.
options is a structure specifying additional options.
Currently, fminunc
recognizes these options:
"FunValCheck"
, "OutputFcn"
, "TolX"
,
"TolFun"
, "MaxIter"
, "MaxFunEvals"
,
"GradObj"
, "FinDiffType"
,
"TypicalX"
, "AutoScaling"
.
If "GradObj"
is "on"
, it specifies that fcn,
called with 2 output arguments, also returns the Jacobian matrix
of right-hand sides at the requested point. "TolX"
specifies
the termination tolerance in the unknown variables, while
"TolFun"
is a tolerance for equations. Default is 1e-7
for both "TolX"
and "TolFun"
.
For description of the other options, see optimset
.
On return, fval contains the value of the function fcn evaluated at x, and info may be one of the following values:
Converged to a solution point. Relative gradient error is less than specified by TolFun.
Last relative step size was less that TolX.
Last relative decrease in function value was less than TolF.
Iteration limit exceeded.
The trust region radius became excessively small.
Optionally, fminunc can also yield a structure with convergence statistics (output), the output gradient (grad) and approximate Hessian (hess).
Notes: If you only have a single nonlinear equation of one variable then
using fminbnd
is usually a much better idea. The algorithm used is a
gradient search which depends on the objective function being differentiable.
If the function has discontinuities it may be better to use a derivative-free
algorithm such as fminsearch
.
See also: fminbnd, fminsearch, optimset.
Find a value of x which minimizes the function fun.
The search begins at the point x0 and iterates using the
Nelder & Mead Simplex algorithm (a derivative-free method). This algorithm
is better-suited to functions which have discontinuities or for which
a gradient-based search such as fminunc
fails.
Options for the search are provided in the parameter options using
the function optimset
. Currently, fminsearch
accepts the
options: "TolX"
, "MaxFunEvals"
, "MaxIter"
,
"Display"
. For a description of these options, see
optimset
.
On exit, the function returns x, the minimum point, and fval, the function value thereof.
Example usages:
fminsearch (@(x) (x(1)-5).^2+(x(2)-8).^4, [0;0]) fminsearch (inline ("(x(1)-5).^2+(x(2)-8).^4", "x"), [0;0])
Previous: Solvers, Up: Nonlinear Equations [Contents][Index]