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
fminsearch. The two
functions use different internal algorithms and some knowledge of the objective
function is required. For functions which can be differentiated,
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
fminbnd recognizes these options:
"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
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
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.
fminunc recognizes these options:
"on", it specifies that fcn,
called with 2 output arguments, also returns the Jacobian matrix
of right-hand sides at the requested point.
the termination tolerance in the unknown variables, while
"TolFun" is a tolerance for equations. Default is
For description of the other options, see
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
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
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
Options for the search are provided in the parameter options using
fminsearch accepts the
"Display". For a description of these options, see
On exit, the function returns x, the minimum point, and fval, the function value thereof.
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])
See also: fminbnd, fminunc, optimset.