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:
- 1 The algorithm converged to a solution.
- 0 Maximum number of iterations or function evaluations has been exhausted.
- -1 The algorithm has been terminated from user output function.
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
orfminsearch
.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 is1e-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:
- 1
- Converged to a solution point. Relative gradient error is less than specified by TolFun.
- 2
- Last relative step size was less that TolX.
- 3
- Last relative decrease in function value was less than TolF.
- 0
- Iteration limit exceeded.
- -3
- 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 asfminsearch
.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, seeoptimset
.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])