R: Constrained Optimization by Linear Approximations
cobyla
R Documentation
Constrained Optimization by Linear Approximations
Description
COBYLA is an algorithm for derivative-free optimization with nonlinear
inequality and equality constraints (but see below).
Usage
cobyla(x0, fn, lower = NULL, upper = NULL, hin = NULL,
nl.info = FALSE, control = list(), ...)
Arguments
x0
starting point for searching the optimum.
fn
objective function that is to be minimized.
lower, upper
lower and upper bound constraints.
hin
function defining the inequality constraints, that is
hin>=0 for all components.
nl.info
logical; shall the original NLopt info been shown.
control
list of options, see nl.opts for help.
...
additional arguments passed to the function.
Details
It constructs successive linear approximations of the objective function
and constraints via a simplex of n+1 points (in n dimensions), and
optimizes these approximations in a trust region at each step.
COBYLA supports equality constraints by transforming them into two
inequality constraints. As this does not give full satisfaction with the
implementation in NLOPT, it has not been made available here.
Value
List with components:
par
the optimal solution found so far.
value
the function value corresponding to par.
iter
number of (outer) iterations, see maxeval.
convergence
integer code indicating successful completion (> 0)
or a possible error number (< 0).
message
character string produced by NLopt and giving additional
information.
Note
The original code, written in Fortran by Powell, was converted in C for the
Scipy project.
References
M. J. D. Powell, “A direct search optimization method that models the
objective and constraint functions by linear interpolation,” in Advances
in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. Hennart
(Kluwer Academic: Dordrecht, 1994), p. 51-67.