optimr: General-purpose optimization

Description Usage Arguments Details Value Source References

View source: R/optimr.R

Description

General-purpose optimization wrapper function that calls other R tools for optimization, including the existing optim() function. optim 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), optimz::optim() does not call the SANN method.

Usage

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optimr(par, fn, gr=NULL, lower=-Inf, upper=Inf, 
            method=NULL, 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?

lower, upper

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

method

A list of the methods to be used. Note that this is an important change from optim() that allows just one method to be specified. See ‘Details’. The default of NULL causes an appropriate set of methods to be supplied depending on the presence or absence of bounds on the parameters. The default unconstrained set is Rvmminu, Rcgminu, lbfgsb3, newuoa and nmkb. The default bounds constrained set is Rvmminb, Rcgminb, lbfgsb3, bobyqa and nmkb.

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.

Details

Note that arguments after ... must be matched exactly.

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.

By default this function 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. DO NOT use both methods.

Possible method codes are 'Nelder-Mead', 'BFGS', 'CG', 'L-BFGS-B', 'nlm', 'nlminb', 'Rcgmin', 'Rvmmin' and 'hjn'. These are in base R or in CRAN repositories or part of this package.

The default methods for unconstrained problems (no lower or upper specified) are an implementation of the Nelder and Mead (1965) and a Variable Metric method based on the ideas of Fletcher (1970) as modified by him in conversation with Nash (1979). Nelder-Mead uses only function values and is robust but relatively slow. It will work reasonably well for non-differentiable functions. The Variable Metric method, "BFGS" updates an approximation to the inverse Hessian using the BFGS update formulas, along with an acceptable point line search strategy. This method appears to work best with analytic gradients. ("Rvmmmin" provides a box-constrained version of this algorithm.

If no method is given, and there are bounds constraints provided, the method is set to "L-BFGS-B".

Method "CG" is a conjugate gradients method based on that by Fletcher and Reeves (1964) (but with the option of Polak–Ribiere or Beale–Sorenson updates). The particular implementation is now dated, and improved yet simpler codes have been implemented. Furthermore, "Rcgmin" allows box constraints as well as fixed (masked) parameters. Conjugate gradient methods will generally be more fragile than the BFGS method, but as they do not store a matrix they may be successful in optimization problems with a large number of parameters.

Method "L-BFGS-B" is that of Byrd et. al. (1995) which allows box constraints, that is each variable can be given a lower and/or upper bound. The initial value must satisfy the constraints. This uses a limited-memory modification of the BFGS quasi-Newton method. If non-trivial bounds are supplied, this method is selected by the original optim() function, with a warning. Unfortunately, the authors of the original Fortran version of this method released a correction for bugs in 2011, but these have not been incorporated into the distributed R codes, which are a C translation of a version that appears to be from the mid-1990s. Conversations with Jorge Nocedal suggest that the bug should NOT affect L-BFGS-B. However, CRAN does have a direct translation of the 2001 Fortran in package lbfgsb3.

Nocedal and Wright (1999) is a comprehensive reference for such methods.

Function fn can return NA or Inf if the function cannot be evaluated at the supplied value, but the initial value must have a computable finite value of fn. However, some methods, of which "L-BFGS-B" is known to be a case, require that the values returned should always be finite.

While optim can be used recursively, and for a single parameter as well as many, this may not be true for optimr. optim also accepts a zero-length par, and just evaluates the function with that argument, but such an input is not recommended.

Method "nlm" is from the package of the same name that implements ideas of Dennis and Schnabel (1983) and Schnabel et al. (1985). See nlm() for more details.

Method "nlminb" is the package of the same name that uses the minimization tools of the PORT library. The PORT documentation is at <URL: http://netlib.bell-labs.com/cm/cs/cstr/153.pdf>. See nlminb() for details. (Though there is very little information about the methods.)

Method "Rcgmin" is from the package of that name. It implements a conjugate gradient algorithm with the Dai and Yuan update (2001) and also allows bounds constraints on the parameters. (Rcgmin also allows mask constraints – fixing individual parameters – but there is as yet no interface from "optimr".)

Method "Rvmmin" is from the package of that name. It implements the same variable metric method as the base optim() function with method "BFGS" but allows bounds constraints on the parameters. (Rvmmin also allows mask constraints – fixing individual parameters – but there is as yet no interface from "optimr".)

Method "hjn" is a conservative implementation of a Hooke and Jeeves (1961)

The control argument is a list that can supply any of the following components:

trace

Non-negative integer. If positive, tracing information on the progress of the optimization is produced. Higher values may produce more tracing information: for method "L-BFGS-B" there are six levels of tracing. trace = 0 gives no output (To understand exactly what these do see the source code: higher levels give more detail.)

follow.on

= TRUE or FALSE. If TRUE, and there are multiple methods, then the last set of parameters from one method is used as the starting set for the next.

save.failures

= TRUE if we wish to keep "answers" from runs where the method does not return convcode==0. FALSE otherwise (default).

maximize

= TRUE if we want to maximize rather than minimize a function. (Default FALSE). Methods nlm, nlminb, ucminf cannot maximize a function, so the user must explicitly minimize and carry out the adjustment externally. However, there is a check to avoid usage of these codes when maximize is TRUE. See fnscale below for the method used in optim that we deprecate.

all.methods

= TRUE if we want to use all available (and suitable) methods.

kkt

=FALSE if we do NOT want to test the Kuhn, Karush, Tucker optimality conditions. The default is TRUE. However, because the Hessian computation may be very slow, we set kkt to be FALSE if there are more than than 50 parameters when the gradient function gr is not provided, and more than 500 parameters when such a function is specified. We return logical values KKT1 and KKT2 TRUE if first and second order conditions are satisfied approximately. Note, however, that the tests are sensitive to scaling, and users may need to perform additional verification. If kkt is FALSE but hessian is TRUE, then KKT1 is generated, but KKT2 is not.

all.methods

= TRUE if we want to use all available (and suitable) methods.

kkttol

= value to use to check for small gradient and negative Hessian eigenvalues. Default = .Machine$double.eps^(1/3)

kkt2tol

= Tolerance for eigenvalue ratio in KKT test of positive definite Hessian. Default same as for kkttol

starttests

= TRUE if we want to run tests of the function and parameters: feasibility relative to bounds, analytic vs numerical gradient, scaling tests, before we try optimization methods. Default is TRUE.

dowarn

= TRUE if we want warnings generated by optimx. Default is TRUE.

badval

= The value to set for the function value when try(fn()) fails. Default is (0.5)*.Machine$double.xmax

usenumDeriv

= TRUE if the numDeriv function grad() is to be used to compute gradients when the argument gr is NULL or not supplied.

The following control elements apply only to some of the methods. The list may be incomplete. See individual packages for details.

fnscale

An overall scaling to be applied to the value of fn and gr during optimization. If negative, turns the problem into a maximization problem. Optimization is performed on fn(par)/fnscale. For methods from the set in optim(). Note potential conflicts with the control maximize.

parscale

A vector of scaling values for the parameters. Optimization is performed on par/parscale and these should be comparable in the sense that a unit change in any element produces about a unit change in the scaled value.For optim.

ndeps

A vector of step sizes for the finite-difference approximation to the gradient, on par/parscale scale. Defaults to 1e-3. For optim.

maxit

The maximum number of iterations. Defaults to 100 for the derivative-based methods, and 500 for "Nelder-Mead".

abstol

The absolute convergence tolerance. Only useful for non-negative functions, as a tolerance for reaching zero.

reltol

Relative convergence tolerance. The algorithm stops if it is unable to reduce the value by a factor of reltol * (abs(val) + reltol) at a step. Defaults to sqrt(.Machine$double.eps), typically about 1e-8. For optim.

alpha, beta, gamma

Scaling parameters for the "Nelder-Mead" method. alpha is the reflection factor (default 1.0), beta the contraction factor (0.5) and gamma the expansion factor (2.0).

REPORT

The frequency of reports for the "BFGS" and "L-BFGS-B" methods if control$trace is positive. Defaults to every 10 iterations for "BFGS" and "L-BFGS-B".

type

for the conjugate-gradients method. Takes value 1 for the Fletcher–Reeves update, 2 for Polak–Ribiere and 3 for Beale–Sorenson.

lmm

is an integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 5.

factr

controls the convergence of the "L-BFGS-B" method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e7, that is a tolerance of about 1e-8.

pgtol

helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed.

Any names given to par will be copied to the vectors passed to fn and gr. Note that no other attributes of par are copied over. (We have not verified this as at 2009-07-29.)

Value

For ‘optim’, a list with components:

par

The best set of parameters found.

value

The value of ‘fn’ corresponding to ‘par’.

counts

A two-element integer vector giving the number of calls to ‘fn’ and ‘gr’ respectively. 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.

convergence

An integer code. ‘0’ indicates successful completion

message

A character string giving any additional information returned by the optimizer, or ‘NULL’.

hessian

Always NULL for this routine.

Source

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

References

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

Dai YH, and Yuan Y (2001). An efficient hybrid conjugate gradient method for unconstrained optimization. Annals of Operations Research 103 (1-4), 33–47.

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.


optimr documentation built on Dec. 18, 2019, 1:36 a.m.