optimr (version 2019-12.16)

opm: General-purpose optimization

Description

General-purpose optimization wrapper function that calls other R tools for optimization, including the existing optim() function. Also tries to unify the calling sequence to allow a number of tools to use the same front-end.

Note that optim() itself allows Nelder--Mead, quasi-Newton and conjugate-gradient algorithms as well as box-constrained optimization via L-BFGS-B. Because SANN does not return a meaningful convergence code (conv), opm() does not call the SANN method, but it can be invoked in optimr().

There is a pseudo-method "ALL" that runs all methods but SANN. Note that this is upper-case.

Usage

opm(par, fn, gr=NULL, hess=NULL, lower=-Inf, upper=Inf, 
            method=c("Nelder-Mead","BFGS"), hessian=FALSE,
            control=list(),
             ...)

Arguments

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.

If 'gr' is NULL, a finite-difference approximation will be used. An open question concerns whether the SAME approximation code used for all methods, or whether there are differences that could/should be examined?

hess

A function to return (as a symmetric matrix) the Hessian of the objective function for those methods that can use this information.

lower, upper

Bounds on the variables for methods such as "L-BFGS-B" that can handle box (or bounds) constraints.

method

A vector of the methods to be used, each as a character string. Note that this is an important change from optim() that allows just one method to be specified. See ‘Details’. If method has just one element, "ALL" (capitalized), all available and appropriate methods will be tried.

hessian

A logical control that if TRUE forces the computation of an approximation to the Hessian at the final set of parameters. If FALSE (default), the hessian is calculated if needed to provide the KKT optimality tests (see kkt in ‘Details’ for the control list). This setting is provided primarily for compatibility with optim().

control

A list of control parameters. See ‘Details’.

…

For optimx further arguments to be passed to fn and gr; otherwise, further arguments are not used.

Value

If there are npar parameters, then the result is a dataframe having one row for each method for which results are reported, using the method as the row name, with columns

par_1, .., par_npar, value, fevals, gevals, niter, convcode, kkt1, kkt2, xtimes

where

par_1

..

par_npar

The best set of parameters found.

value

The value of fn corresponding to par.

fevals

The number of calls to fn.

gevals

The number of calls to gr. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.

niter

For those methods where it is reported, the number of ``iterations''. See the documentation or code for particular methods for the meaning of such counts.

convcode

An integer code. 0 indicates successful convergence. Various methods may or may not return sufficient information to allow all the codes to be specified. An incomplete list of codes includes

1

indicates that the iteration limit maxit had been reached.

20

indicates that the initial set of parameters is inadmissible, that is, that the function cannot be computed or returns an infinite, NULL, or NA value.

21

indicates that an intermediate set of parameters is inadmissible.

10

indicates degeneracy of the Nelder--Mead simplex.

51

indicates a warning from the "L-BFGS-B" method; see component message for further details.

52

indicates an error from the "L-BFGS-B" method; see component message for further details.

kkt1

A logical value returned TRUE if the solution reported has a ``small'' gradient.

kkt2

A logical value returned TRUE if the solution reported appears to have a positive-definite Hessian.

xtimes

The reported execution time of the calculations for the particular method.

The attribute "details" to the returned answer object contains information, if computed, on the gradient (ngatend) and Hessian matrix (nhatend) at the supposed optimum, along with the eigenvalues of the Hessian (hev), as well as the message, if any, returned by the computation for each method, which is included for each row of the details. If the returned object from optimx() is ans, this is accessed via the construct attr(ans, "details")

This object is a matrix based on a list so that if ans is the output of optimx then attr(ans, "details")[1, ] gives the first row and attr(ans,"details")["Nelder-Mead", ] gives the Nelder-Mead row. There is one row for each method that has been successful or that has been forcibly saved by save.failures=TRUE.

There are also attributes

maximize

to indicate we have been maximizing the objective

npar

to provide the number of parameters, thereby facilitating easy extraction of the parameters from the results data frame

follow.on

to indicate that the results have been computed sequentially, using the order provided by the user, with the best parameters from one method used to start the next. There is an example (ans9) in the script ox.R in the demo directory of the package.

Details

This routine is essentially the same as that in package optimrx which is NOT in CRAN. This version permits the selection of fewer optimizers in the method argument. This reduced selection is intended to avoid failures if dependencies are not available. The available methods are listed in the variable allmeth in the file ctrldefault.R.

Note that arguments after … must be matched exactly.

See the manual for function optimr().

References

See the manual pages for optim() and the packages the DESCRIPTION suggests.

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/.

Nash JC (2014). On Best Practice Optimization Methods in R., Journal of Statistical Software, 60(2), 1-14., URL http://www.jstatsoft.org/v60/i02/.

See Also

nlm, nlminb, Rcgmin, Rvmmin, optimize for one-dimensional minimization; constrOptim for linearly constrained optimization.

Examples

# NOT RUN {
require(graphics)
cat("Note possible demo(ox) for extended examples\n")


## Show multiple outputs of optimx using all.methods
# genrose function code
genrose.f<- function(x, gs=NULL){ # objective function
## One generalization of the Rosenbrock banana valley function (n parameters)
	n <- length(x)
        if(is.null(gs)) { gs=100.0 }
	fval<-1.0 + sum (gs*(x[1:(n-1)]^2 - x[2:n])^2 + (x[2:n] - 1)^2)
        return(fval)
}

genrose.g <- function(x, gs=NULL){
# vectorized gradient for genrose.f
# Ravi Varadhan 2009-04-03
	n <- length(x)
        if(is.null(gs)) { gs=100.0 }
	gg <- as.vector(rep(0, n))
	tn <- 2:n
	tn1 <- tn - 1
	z1 <- x[tn] - x[tn1]^2
	z2 <- 1 - x[tn]
	gg[tn] <- 2 * (gs * z1 - z2)
	gg[tn1] <- gg[tn1] - 4 * gs * x[tn1] * z1
	return(gg)
}

genrose.h <- function(x, gs=NULL) { ## compute Hessian
   if(is.null(gs)) { gs=100.0 }
	n <- length(x)
	hh<-matrix(rep(0, n*n),n,n)
	for (i in 2:n) {
		z1<-x[i]-x[i-1]*x[i-1]
		z2<-1.0-x[i]
                hh[i,i]<-hh[i,i]+2.0*(gs+1.0)
                hh[i-1,i-1]<-hh[i-1,i-1]-4.0*gs*z1-4.0*gs*x[i-1]*(-2.0*x[i-1])
                hh[i,i-1]<-hh[i,i-1]-4.0*gs*x[i-1]
                hh[i-1,i]<-hh[i-1,i]-4.0*gs*x[i-1]
	}
        return(hh)
}

startx<-4*seq(1:10)/3.
ans8<-opm(startx,fn=genrose.f,gr=genrose.g, hess=genrose.h, 
   control=list(all.methods=TRUE, save.failures=TRUE, trace=1), gs=10)
ans8
ans8[, "gevals"]
ans8["spg", ]
summary(ans8, par.select = 1:3)
summary(ans8, order = value)[1, ] # show best value
head(summary(ans8, order = value)) # best few
## head(summary(ans8, order = "value")) # best few -- alternative syntax

## order by value.  Within those values the same to 3 decimals order by fevals.
## summary(ans8, order = list(round(value, 3), fevals), par.select = FALSE)
summary(ans8, order = "list(round(value, 3), fevals)", par.select = FALSE)

## summary(ans8, order = rownames, par.select = FALSE) # order by method name
summary(ans8, order = "rownames", par.select = FALSE) # same

summary(ans8, order = NULL, par.select = FALSE) # use input order
## summary(ans8, par.select = FALSE) # same

# }