| Title: | Derivative-Free Optimization Algorithms by Quadratic Approximation |
|---|---|
| Description: | Derivative-free optimization by quadratic approximation based on an interface to Fortran implementations by M. J. D. Powell. |
| Authors: | Douglas Bates [aut], Katharine M. Mullen [aut, cre], John C. Nash [aut], Ravi Varadhan [aut] |
| Maintainer: | Katharine M. Mullen <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2.8 |
| Built: | 2024-10-31 22:24:26 UTC |
| Source: | CRAN |
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.
bobyqa(par, fn, lower = -Inf, upper = Inf, control = list(), ...)bobyqa(par, fn, lower = -Inf, upper = Inf, control = list(), ...)
par |
A numeric vector of starting estimates of the parameters of the objective function. |
fn |
A function that returns the value of the objective at the
supplied set of parameters |
lower |
A numeric vector of lower bounds on the parameters. If the length is 1 the single lower bound is applied to all parameters. |
upper |
A numeric vector of upper bounds on the parameters. If the length is 1 the single upper bound is applied to all parameters. |
control |
An optional list of control settings. See the details section for the names of the settable control values and their effect. |
... |
Further arguments to be passed to |
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:
The number of points used to approximate the objective function
via a quadratic approximation. The value of npt must be in the
interval where is the number of
parameters in par. Choices that exceed are not
recommended. If not defined, it will be set to .
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.
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.
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.
The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.
A list with components:
par |
The best set of parameters found. |
fval |
The value of the objective at the best set of parameters found. |
feval |
The number of function evaluations used. |
ierr |
An integer error code. A value of zero indicates success. Other values are
|
msg |
A message describing the outcome of UOBYQA |
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.
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.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.
The purpose of newuoa is to minimize a function of many variables
by a trust region method that forms quadratic models by interpolation.
newuoa(par, fn, control = list(), ...)newuoa(par, fn, control = list(), ...)
par |
A numeric vector of starting estimates. |
fn |
A function that returns the value of the objective at the
supplied set of parameters |
control |
An optional list of control settings. See the details section for the names of the settable control values and their effect. |
... |
Further arguments to be passed to |
Functions fn must return a numeric value.
The control argument is a list; possible named values in the
list and their defaults are:
The number of points used to approximate the objective function
via a quadratic approximation. The value of npt must be in the
interval where is the number of
parameters in par. Choices that exceed are not
recommended. If not defined, it will be set to .
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)
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.
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.
The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.
A list with components:
par |
The best set of parameters found. |
fval |
The value of the objective at the best set of parameters found. |
feval |
Number of function evaluations to determine the optimum |
ierr |
An integer error code. A value of zero indicates success. Other values (consistent with BOBYQA values) are
|
msg |
A message describing the outcome of UOBYQA |
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.
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.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.
The purpose of uobyqa is to minimize a function of many variables
by a trust region method that forms quadratic models by interpolation.
uobyqa(par, fn, control = list(), ...)uobyqa(par, fn, control = list(), ...)
par |
A numeric vector of starting estimates. |
fn |
A function that returns the value of the objective at the
supplied set of parameters |
control |
An optional list of control settings. See the details section for the names of the settable control values and their effect. |
... |
Further arguments to be passed to |
Functions fn must return a numeric value.
The control argument is a list. Possible named values in the
list and their defaults are:
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.
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.
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.
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.
A list with components:
par |
The best set of parameters found. |
fval |
The value of the objective at the best set of parameters found. |
feval |
The number of function evaluations used. |
ierr |
An integer error code. A value of zero indicates success. Other values (consistent with BOBYQA values) are
|
msg |
A message describing the outcome of UOBYQA |
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.
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.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.