General-purpose optimization
General-purpose optimization wrapper function that calls other R tools for optimization, including the existing optim() function. optimr also tries to unify the calling sequence to allow a number of tools to use the same front-end, in fact using the calling sequence of the R function optim().
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optimr(par, fn, gr=NULL, hess=NULL, method=NULL, lower=-Inf, upper=Inf, hessian=FALSE, control=list(), ...)
par: a vector of initial values for the parameters for which optimal values are to be found. Names on the elements of this vector are preserved and used in the results data frame.
fn: A function to be minimized (or maximized), with first argument the vector of parameters over which minimization is to take place. It should return a scalar result.
gr: A function to return (as a vector) the gradient for those methods that can use this information. The first argument of this function is the supplied set of parameters par, with auxiliary data in .... This function returns the gradient as a numeric vector.
If gr is NULL, then this is passed forward and whatever default action is specified for the chosen method for the case of a null gradient code is used. For many methods, this is a finite-difference approximation, but some methods require user input for the gradient and will fail otherwise. In such cases, we try to return convergence of 9998.
If gr is a character string, then that string is taken as the name of a gradient approximation function, for example, "grfwd", "grback" and "grcentral" for standard forward, backward and central approximations. Method "grnd" uses the grad() function from package numDeriv. Method "grpracma" uses the approximation from package pracma.
The use of numerical gradients is generally discouraged, and particularly for ncg, Rcgmin, nvm and Rvmmin. First, the termination tests use a size measure on the gradient, and numerical gradient approximations can sometimes give results that are too large. Second, if there are bounds constraints, the step(s) taken to calculate the approximation to the derivative are NOT checked to see if they are out of bounds, and the function may be undefined at the evaluation point. If an approximation must be used, "grcentral" is recommended in the absence of other considerations.
Note that all but the grnd routine use a stepsize parameter that can be redefined in a special environment optsp in variable deps. The default is optsp$deps = 1e-06. However, redefining this is discouraged unless you understand what you are doing.
hess: A function to return (as a matrix) the hessian for those methods that can use this information. At time of writing, quoted arguments (as for gr) are not offered as a mechanism for providing a numerical approximation.
If hess is NULL, then this is passed forward and whatever default action is specified for the chosen method for the case of a null gradient code is used.
lower, upper: Bounds on the variables for methods such as "L-BFGS-B" that can handle box (or bounds) constraints. A small set of methods can handle masks, that is, fixed parameters, and these can be specified by making the lower and upper bounds equal to the starting value. (It is possible that the starting value could be different from the lower/upper bounds set, but this behaviour has NOT yet been defined and users are cautioned.)
method: A character string giving the name of the optimization method to be applied. See the list allmeth in file ctrldefault.R which is part of this package.
hessian: A logical control that if TRUE forces the computation of an approximation to the Hessian at the final set of parameters. Note that this will NOT necessarily use the same approximation as may be provided by the method called. Instead, the function hessian() from package numDeriv is used if no gradient gr is supplied, else the function jacobian() from numDeriv
is applied to the gradient function gr.
control: A list of control parameters. See Details .
...: Further arguments to be passed to fn
and gr if needed for computation of these quantities; otherwise, further arguments are not used.
Note that arguments after ... should be matched exactly.
By default optimr performs minimization, but it will maximize if control$maximize is TRUE. The original optim() function allows control$fnscale to be set negative to accomplish this, and this control can be used with optimr but is deprecated. Moreover, if control$maximize is set, it will take precedence over control$fnscale. Generally it is a BAD IDEA to use both mechanisms simultaneously.
Possible method choices are specified by the list allmeth in the file ctrldefault.R which is part of this package.
If no method is specified, the method specified by defmethod in file ctrldefault.R (which is part of this package) will be attempted.
Function fn must return a finite scalar value at the initial set of parameters. Some methods can handle a returned value NA or Inf
if the function cannot be evaluated at the supplied value. However, other methods, of which "L-BFGS-B" is known to be a case, require that the values returned should always be finite. It is recommended that user functions ALWAYS return a usable value. Note that the control badval in ctrldefault.R give a possible number that could be returned.
For details of methods, please consult the documentation of the individual methods. (The NAMESPACE file lists the packages from which functions are imported.) Note that method "hjn" is a conservative implementation of a Hooke and Jeeves (1961) and is part of this package. It is provided as a simple example of a very crude optimization method; it is NOT intended as a production method, but may be useful for didactic purposes.
The control argument is a list that can supply any of the components in the file ctrldefault.R which is part of this package. It may supply controls that are useful or required for particular methods, but users are warned to be careful to ensure that extraneous or incorrect components and values are not passed. Some control elements apply only to some methods. See individual packages for details. optimr does not support all the possible controls for all methods.
A particular case is the method "bobyqa", where the control rhobeg=0
gives a set of controls that depend on the bounds supplied. This choice is only in the current package. Unspecified or negative control rhobeg=0
gives the minqa defaults. Positive value of this control (and optionally control rhoend) supply those values. See inst/doc/examples/specctrlhobbs.R.
Any names given to par will be copied to the vectors passed to fn and gr. Apparently no other attributes of par
are copied over, but this may need to be verified, especially if parameters are passed to non-R routines.
CAUTION: because there is a seldom-used parameter hess, you should NOT make a call like
ans <- optimr(start, myf, myg, lower, upper)
or you will likely get wrong results. Instead use
ans <- optimr(start, myf, myg, lower=lower, upper=upper)
A list with components:
lbfgs.opm() gives some other possible values and their meaning.# Simple Test Function 1: simfun.f = function(x) { fun <- sum(x^2 ) ## if (trace) ... to be fixed print(c(x = x, fun = fun)) fun } simfun.g = function(x) { grad<-2.0*x grad } simfun.h = function(x) { n<-length(x) t<-rep(2.0,n) hess<-diag(t) } # library(optimx) ## May be needed for independent running. strt <- c(1,2,3) ansfgh <- optimr(strt, simfun.f, simfun.g, simfun.h, method="nlm", hessian=TRUE, control=list(trace=2)) proptimr(ansfgh) # compact output of result cat("nlm does not return good counts\n") cat("ansfgh$counts:") print(ansfgh$counts)
See the manual pages for optim().
Hooke R. and Jeeves, TA (1961). Direct search solution of numerical and statistical problems. Journal of the Association for Computing Machinery (ACM). 8 (2): 212–229.
Nash JC, and Varadhan R (2011). Unifying Optimization Algorithms to Aid Software System Users: optimx for R., Journal of Statistical Software, 43(9), 1-14., URL http://www.jstatsoft.org/v43/i09/.
Nocedal J, and Wright SJ (1999). Numerical optimization. New York: Springer. 2nd Edition 2006.