Compatibility frontend for nonlinear minimization of a scalar objective function.
This function is for Matlab compatibility and provides a subset of
the functionality of nonlin_min.
objf: objective function. It gets the real parameters as argument.
x0: real vector or array of initial parameters.
A, b: Inequality constraints of the parameters p
with A * p - b <= 0.
Aeq, beq: Equality constraints of the parameters p
with A * p - b = 0.
lb, ub: Bounds of the parameters p with lb
<= p <= ub. Vectors or arrays. If the number of elements is
smaller than the number of parameters, as many bounds as present
are applied, starting with the first parameter. This is for
compatibility with Matlab.
nonlcon: Nonlinear constraints. Function returning the
current values of nonlinear inequality constraints (constrained to
<= 0) in the first output and the current values of nonlinear
equality constraints in the second output.
options: structure whose fields stand for optional settings
referred to below. The fields can be set by optimset().
An argument can be set to [] to indicate that its value is
not set.
fmincon may also be called with a single structure
argument with the fields objective, x0, Aineq,
bineq, Aeq, beq, lb, ub,
nonlcon and options, resembling
the separate input arguments above. Additionally,
the structure must have the field solver, set to
"fmincon".
The returned values are the final parameters x, the final
value of the objective function fval, an integer cvg
indicating if and how optimization succeeded or failed, and a
structure outp with additional information, curently with
possible fields: iterations, the number of iterations,
funcCount, the number of objective function calls (indirect
calls by gradient function not counted), constrviolation,
the maximum of the constraint violations. The backend may define
additional fields. cvg is greater than zero for success and
less than or equal to zero for failure; its possible values depend
on the used backend and currently can be 0 (maximum number
of iterations exceeded), 1 (success without further
specification of criteria), 2 (parameter change less than
specified precision in two consecutive iterations), 3
(improvement in objective function less than specified), -1
(algorithm aborted by a user function), or -4 (algorithm got
stuck).
Algorithminterior-point, sqp, and sqp-legacy are
mapped to optims lm_feasible algorithm (the default) to
satisfy constraints throughout the optimization. active-set
is mapped to octave_sqp, which may perform better if
constraints only need to be satisfied for the result. Other
algorithms are available with nonlin_min.
OutputFcnSimilar to the setting user_interaction — see
optim_doc(). Differently, OutputFcn returns only one
output argument, the stop flag.
GradObjIf set to "on", objf must return the gradient of the
objective function as a second output. The default is "off".
GradConstrIf set to "on", nonlcon must return the Jacobians of
the inequality- and equality-constraints as third and fourth
output, respectively.
HessianFcnIf set to "objective", objf must not only return the
gradient as the second, but also the Hessian as the third output.
Display, FinDiffRelStep, FinDiffType, TypicalX, MaxIter, TolFun, TolX,See documentation of these options in optim_doc().
For description of individual backends, type
optim_doc ("scalar optimization") and choose the backend in
the menu.
The following code
## Example for default optimization (Levenberg/Marquardt with
## BFGS), one non-linear equality constraint. Constrained optimum is
## at p = [0; 1].
objective_function = @ (p) p(1)^2 + p(2)^2;
pin = [-2; 5];
constraint_function = @ (p) - (p(1)^2 + 1 - p(2));
[p, objf, cvg, outp] = fmincon (objective_function, pin, [], [], [], [], [], [], @ (p) {[], constraint_function(p)}{:})
Produces the following output
p =
-1.0909e-08
1.0000e+00
objf = 1.0000
cvg = 3
outp =
scalar structure containing the fields:
user_interaction =
scalar structure containing the fields:
stop = [](0x1)
info = {}(0x1)
niter = 7
nobjf = 12
constrviolation = 2.1094e-15
Package: optim