General-purpose optimization


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. These include spg from the BB package, ucminf, nlm, and nlminb. 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.


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



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.


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.


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.


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.


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().


A list of control parameters. See ‘Details’.


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


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

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', 'spg', 'ucminf', 'newuoa', 'bobyqa', 'nmkb', 'hjkb', 'Rcgmin', 'lbfgsb3' or 'Rvmmin'. These are in base R or in CRAN repositories. From R-forge, method 'Rtnmin' is available. Other methods are likely to be added over time.

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. While it seems the errors affect very few computations, users may wish to use the Fortran codes in package lbfgsb3.

Nocedal and Wright (1999) is a comprehensive reference for the previous three 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 optimx. optim also accepts a zero-length par, and just evaluates the function with that argument.

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:>. See nlminb() for details. (Though there is very little information about the methods.)

Method "spg" is from package BB implementing a spectral projected gradient method for large-scale optimization with simple constraints due R adaptation, with significant modifications, by Ravi Varadhan, Johns Hopkins University (Varadhan and Gilbert, 2009), from the original FORTRAN code of Birgin, Martinez, and Raydan (2001).

Method "Rcgmin" is from the package of that name. It implements a conjugate gradient algorithm with the Yuan/Dai update (ref??) 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 "Rtnmin" is from the package of that name. It implements a truncated Newton method of Stephen Nash translated from Matlab. It allows bounds constraints on the parameters.

Methods "bobyqa", "uobyqa" and "newuoa" are from the package "minqa" which implement optimization by quadratic approximation routines of the similar names due to M J D Powell (2009). See package minqa for details. Note that "uobyqa" and "newuoa" are for unconstrained minimization, while "bobyqa" is for box constrained problems. While "uobyqa" may be specified, it is NOT part of the all.methods = TRUE set.

Methods "nmkb" and "hjkb" are from package dfoptim. They implement respectively variants of the Nelder-Mead and Hooke and Jeeves derivative-free methods, but both allow bounds constraints. However, it is important to note that "nmkb" must NOT have starting parameters on a lower or upper bound, as a transformation of the paramters is used to effect the constraints.

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


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.)


= 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.


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


= 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.


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


=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.


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


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


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


= 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.


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


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


= 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.


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.


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.


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


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


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


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).


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".


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


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


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.


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.)


For ‘optim’, a list with components:


The best set of parameters found.


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


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.


An integer code. ‘0’ indicates successful completion


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


Always NULL for this routine.


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


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

?? Nocedal

?? Yuan and Dai

comments powered by Disqus