function to be maximised. Must have the parameter vector as the first argument. In order to use numeric gradient and BHHH method, fn must return a vector of observation-specific likelihood values. Those are summed internally where necessary. If the parameters are out of range, fn should return NA. See details for constant parameters.

gradient of fn. Must have the parameter vector as the first argument. If NULL, numeric gradient is used (maxNM and maxSANN do not use gradient). Gradient may return a matrix, where columns correspond to the parameters and rows to the observations (useful for maxBHHH). The columns are summed internally.

Hessian of fn. Not used by any of these methods, included for compatibility with maxNR.

initial values for the parameters. If start values are named, those names are also carried over to the results.

parameters to be treated as constants at their start values. If present, it is treated as an index vector of start parameters.

list of control parameters or a ‘MaxControl’ object. If it is a list, the default values are used for the parameters that are left unspecified by the user. These functions accept the following parameters:

reltol

sqrt(.Machine$double.eps), stopping condition. Relative convergence tolerance: the algorithm stops if the relative improvement between iterations is less than ‘reltol’. Note: for compatibility reason ‘tol’ is equivalent to ‘reltol’ for optim-based optimizers.

iterlim

integer, maximum number of iterations. Default values are 200 for ‘BFGS’, 500 (‘CG’ and ‘NM’), and 10000 (‘SANN’). Note that ‘iteration’ may mean different things for different optimizers.

printLevel

integer, larger number prints more working information. Default 0, no information.

nm_alpha

1, Nelder-Mead simplex method reflection coefficient (see Nelder & Mead, 1965)

nm_beta

0.5, Nelder-Mead contraction coefficient

nm_gamma

2, Nelder-Mead expansion coefficient

sann_cand

NULL or a function for "SANN" algorithm to generate a new candidate point; if NULL, Gaussian Markov kernel is used (see argument gr of optim).

sann_temp

10, starting temperature for the “SANN” cooling schedule. See optim.

sann_tmax

10, number of function evaluations at each temperature for the “SANN” optimizer. See optim.

sann_randomSeed

123, integer to seed random numbers to ensure replicability of “SANN” optimization and preserve R random numbers. Use options like sann_randomSeed=Sys.time() or sann_randomSeed=sample(100,1) if you want stochastic results.

either NULL for unconstrained optimization or a list with two components. The components may be either eqA and eqB for equality-constrained optimization A %*% theta + B = 0; or ineqA and ineqB for inequality constraints A %*% theta + B > 0. More than one row in ineqA and ineqB corresponds to more than one linear constraint, in that case all these must be zero (equality) or positive (inequality constraints). The equality-constrained problem is forwarded to sumt, the inequality-constrained case to constrOptim2.

how (and if) to calculate the final Hessian. Either FALSE (not calculate), TRUE (use analytic/numeric Hessian) or "bhhh"/"BHHH" for information equality approach. The latter approach is only suitable for maximizing log-likelihood function. It requires the gradient/log-likelihood to be supplied by individual observations, see maxBHHH for details.

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. (see optim)

further arguments for fn and grad.

fn value at maximum (the last calculated value if not converged.)

estimated parameter value.

vector, last calculated gradient value. Should be close to 0 in case of normal convergence.

matrix of gradients at parameter value estimate evaluated at each observation (only if grad returns a matrix or grad is not specified and fn returns a vector).

Hessian at the maximum (the last calculated value if not converged).

integer. Success code, 0 is success (see optim).

a short message, describing the return code.

logical vector, which parameters are optimized over. Contains only TRUE-s if no parameters are fixed.

number of iterations. 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.

character string, type of maximization.

the optimization control parameters in the form of a MaxControl object.

A list, describing the constrained optimization (NULL if unconstrained). Includes the following components:

type

type of constrained optimization

outer.iterations

number of iterations in the constraints step

barrier.value

value of the barrier function