An R interface to the bobyqa implementation of Powell

Description

The purpose of bobyqa is to minimize a function of many variables by a trust region method that forms quadratic models by interpolation. Box constraints (bounds) on the parameters are permitted.

Usage

bobyqa(par, fn, lower = -Inf, upper = Inf, control = list(), ...)

Arguments

Details

The function fn must return a scalar numeric value.

The control argument is a list. Possible named values in the list and their defaults are:

npt

The number of points used to approximate the objective function via a quadratic approximation. The value of npt must be in the interval [n+2,(n+1)(n+2)/2] where n is the number of parameters in par. Choices that exceed 2*n+1 are not recommended. If not defined, it will be set to \min(n * 2, n+2).

rhobeg

rhobeg and rhoend must be set to the initial and final values of a trust region radius, so both must be positive with 0 < rhoend < rhobeg. Typically rhobeg should be about one tenth of the greatest expected change to a variable. If the user does not provide a value, this will be set to min(0.95, 0.2 * max(abs(par))). Note also that smallest difference abs(upper-lower) should be greater than or equal to rhobeg*2. If this is not the case then rhobeg will be adjusted.

rhoend

The smallest value of the trust region radius that is allowed. If not defined, then 1e-6 times the value set for rhobeg will be used.

iprint

The value of iprint should be set to an integer value in 0, 1, 2, 3, ..., which controls the amount of printing. Specifically, there is no output if iprint=0 and there is output only at the start and the return if iprint=1. Otherwise, each new value of rho is printed, with the best vector of variables so far and the corresponding value of the objective function. Further, each new value of the objective function with its variables are output if iprint=3. If iprint > 3, the objective function value and corresponding variables are output every iprint evaluations. Default value is 0.

maxfun

The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.

Value

A list with components:

References

M. J. D. Powell (2007) "Developments of NEWUOA for unconstrained minimization without derivatives", Cambridge University, Department of Applied Mathematics and Theoretical Physics, Numerical Analysis Group, Report NA2007/05, http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2007_05.pdf.

M. J. D. Powell (2009), "The BOBYQA algorithm for bound constrained optimization without derivatives", Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge, UK. http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf.

Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.

See Also

optim, nlminb

Examples

fr <- function(x) {   ## Rosenbrock Banana function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x1 <- bobyqa(c(1, 2), fr, lower = c(0, 0), upper = c(4, 4)))
## => optimum at c(1, 1) with fval = 0

str(x1)  # see that the error code and msg are returned

# check the error exits
# too many iterations
x1e<-bobyqa(c(1, 2), fr, lower = c(0, 0), upper = c(4, 4), control = list(maxfun=50))
str(x1e)

# Throw an error because bounds too tight
x1b<-bobyqa(c(4,4), fr, lower = c(0, 3.9999999), upper = c(4, 4))
str(x1b)

# Throw an error because npt is too small -- does NOT work as of 2010-8-10 as 
#    minqa.R seems to force a reset.
x1n<-bobyqa(c(2,2), fr, lower = c(0, 0), upper = c(4, 4), control=list(npt=1))
str(x1n)

# To add if we can find them -- examples of ierr = 3 and ierr = 5.

An R interface to the NEWUOA implementation of Powell

Description

The purpose of newuoa is to minimize a function of many variables by a trust region method that forms quadratic models by interpolation.

Usage

newuoa(par, fn, control = list(), ...)

Arguments

Details

Functions fn must return a numeric value. The control argument is a list; possible named values in the list and their defaults are:

npt

The number of points used to approximate the objective function via a quadratic approximation. The value of npt must be in the interval [n+2,(n+1)(n+2)/2] where n is the number of parameters in par. Choices that exceed 2*n+1 are not recommended. If not defined, it will be set to \min(n * 2, n+2).

rhobeg

rhobeg and rhoend must be set to the initial and final values of a trust region radius, so both must be positive with 0 < rhoend < rhobeg. Typically rhobeg should be about one tenth of the greatest expected change to a variable. If the user does not provide a value, this will be set to max(par) / 2)

rhoend

The smallest value of the trust region radius that is allowed. If not defined, then 1e-6 times the value set for rhobeg will be used.

iprint

The value of iprint should be set to an integer value in 0, 1, 2, 3, ..., which controls the amount of printing. Specifically, there is no output if iprint=0 and there is output only at the start and the return if iprint=1. Otherwise, each new value of rho is printed, with the best vector of variables so far and the corresponding value of the objective function. Further, each new value of the objective function with its variables are output if iprint=3. If iprint > 3, the objective function value and corresponding variables are output every iprint evaluations. Default value is 0.

maxfun

The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.

Value

A list with components:

References

M. J. D. Powell, "The NEWUOA software for unconstrained optimization without derivatives", in Large-Scale Nonlinear Optimization, Series: Nonconvex Optimization and Its Applications , Vol. 83, Di Pillo, Gianni; Roma, Massimo (Eds.) 2006, New York: Springer US.

M. J. D. Powell, "Developments of NEWUOA for minimization without derivatives" IMA Journal of Numerical Analysis, 2008; 28: 649-664.

M. J. D. Powell (2007) "Developments of NEWUOA for unconstrained minimization without derivatives" Cambridge University, Department of Applied Mathematics and Theoretical Physics, Numerical Analysis Group, Report NA2007/05, http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2007_05.pdf.

Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.

See Also

optim, nlminb

Examples

fr <- function(x) {   ## Rosenbrock Banana function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x2 <- newuoa(c(1, 2), fr))
## => optimum at c(1, 1) with fval = 0

# check the error exits
# too many iterations
x2e<-newuoa(c(1, 2), fr, control = list(maxfun=50))
str(x2e)

# Throw an error because npt is too small -- does NOT work as of 2010-8-10 as 
#    minqa.R seems to force a reset.
x2n<-newuoa(c(2,2), fr, control=list(npt=1))
str(x2n)

# To add if we can find them -- examples of ierr = 3 and ierr = 5.

An R interface to the uobyqa implementation of Powell

Description

The purpose of uobyqa is to minimize a function of many variables by a trust region method that forms quadratic models by interpolation.

Usage

uobyqa(par, fn, control = list(), ...)

Arguments

Details

Functions fn must return a numeric value.

The control argument is a list. Possible named values in the list and their defaults are:

rhobeg

rhobeg and rhoend must be set to the initial and final values of a trust region radius, so both must be positive with 0 < rhoend < rhobeg. Typically rhobeg should be about one tenth of the greatest expected change to a variable.

rhoend

The smallest value of the trust region radius that is allowed. If not defined, then 1e-6 times the value set for rhobeg will be used.

iprint

The value of iprint should be set to an integer value in 0, 1, 2, 3, ..., which controls the amount of printing. Specifically, there is no output if iprint=0 and there is output only at the start and the return if iprint=1. Otherwise, each new value of rho is printed, with the best vector of variables so far and the corresponding value of the objective function. Further, each new value of the objective function with its variables are output if iprint=3. If iprint > 3, the objective function value and corresponding variables are output every iprint evaluations. Default value is 0.

maxfun

The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.

Powell's Fortran code has been slightly modified (thanks to Doug Bates for help on this) to avoid use of PRINT statements. Output is now via calls to C routines set up to work with the routines BOBYQA, NEWUOA and UOBYQA.

Value

A list with components:

References

M. J. D. Powell, "The uobyqa software for unconstrained optimization without derivatives", in Large-Scale Nonlinear Optimization, Series: Nonconvex Optimization and Its Applications , Vol. 83, Di Pillo, Gianni; Roma, Massimo (Eds.) 2006, New York: Springer US.

M. J. D. Powell, "Developments of uobyqa for minimization without derivatives", IMA Journal of Numerical Analysis, 2008; 28: 649-664.

Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.

See Also

optim, nlminb

Examples

fr <- function(x) {   ## Rosenbrock Banana function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x3 <- uobyqa(c(1, 2), fr))
## => optimum at c(1, 1) with fval = 0
# check the error exits
# too many iterations
x3e<-uobyqa(c(1, 2), fr, control = list(maxfun=50))
str(x3e)


# To add if we can find them -- examples of ierr = 3.