Bound Optimization by Quadratic Approximation
BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function.
bobyqa(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...)
x0 |
starting point for searching the optimum. |
fn |
objective function that is to be minimized. |
lower, upper |
lower and upper bound constraints. |
nl.info |
logical; shall the original NLopt info been shown. |
control |
list of options, see |
... |
additional arguments passed to the function. |
This is an algorithm derived from the BOBYQA Fortran subroutine of Powell, converted to C and modified for the NLOPT stopping criteria.
List with components:
par |
the optimal solution found so far. |
value |
the function value corresponding to |
iter |
number of (outer) iterations, see |
convergence |
integer code indicating successful completion (> 0) or a possible error number (< 0). |
message |
character string produced by NLopt and giving additional information. |
Because BOBYQA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.
M. J. D. Powell. “The BOBYQA algorithm for bound constrained optimization without derivatives,” Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009).
fr <- function(x) { ## Rosenbrock Banana function
100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(S <- bobyqa(c(0, 0, 0), fr, lower = c(0, 0, 0), upper = c(0.5, 0.5, 0.5)))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.