Unified optimisation interface with structured parameters and parallel numerical gradients

optim2() provides a unified interface to multiple deterministic and stochastic optimisation methods, combining the algorithms available through stats::optim() with a small set of additional solvers accessed via calibrar's internal dispatcher.

Usage

optim2(
  par,
  fn,
  gr = NULL,
  ...,
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent", "nlm", "nlminb",
    "Rcgmin", "Rvmmin", "hjn", "spg", "LBFGSB3", "AHR-ES"),
  lower = -Inf,
  upper = +Inf,
  active = NULL,
  control = list(),
  hessian = FALSE,
  parallel = FALSE
)

Arguments

par: A numeric vector or list. The length of par defines the number of parameters to be estimated (i.e., the dimension of the problem).
fn: The objective function to be minimised. It should accept a parameter vector (or list, depending on the wrapper) as first argument and return either a scalar value (single-objective) or a numeric vector (multi-objective).
gr: A function computing the gradient of fn. If NULL, a numerical approximation is used. Alternatively, a character string can specify the numerical gradient scheme: "central", "forward" (default), "backward", or "richardson".
...: Additional arguments passed to fn and gr.
method: Optimisation method(s) to be used. Can be a single method name or a vector of method names (e.g., one per phase). If NULL, a default is chosen based on replicates (see Details).
lower: Lower bounds for parameters. One value or a vector of the same length as par. NA is treated as -Inf. Default is unconstrained.
upper: Upper bounds for parameters. One value or a vector of the same length as par. NA is treated as Inf. Default is unconstrained.
active: Boolean vector of the same length as par, indicating if the parameter is used in the optimisation (TRUE) or held at a fixed value (FALSE).
control: A list of control options. Common options include ncores, run, master, verbose, REPORT, restart.file, gradient, and gr.method. Additional solver-specific options may be passed through to the underlying optimiser.
hessian: Logical. Should a numerically differentiated Hessian matrix be returned? Currently not implemented.
parallel: Logical. Enable parallel computation (e.g., for replicated evaluations and/or numerical gradients) using up to control$ncores cores.

Value

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: Only if argument hessian is TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.

Details

Methods. The current selection includes (i) base stats::optim() methods, (ii) additional gradient-based solvers from external packages, and (iii) heuristic/global methods.

Comparability. Not all methods are directly comparable: some are deterministic local optimisers (e.g., quasi-Newton), others are derivative-free local searches, and others are stochastic/global heuristics. Method choice should reflect the objective function (smooth vs. non-smooth, deterministic vs. stochastic) and the presence of constraints.

Control arguments. optim2() standardises a set of common control arguments (e.g., iteration limits, tolerances, tracing, and scaling) where supported, while still allowing method-specific control parameters to be passed through to the underlying solver.

Parallel numerical gradients. When analytic gradients are not provided, optim2() can compute finite-difference numerical gradients and distribute function evaluations across multiple cores, which can substantially reduce wall-clock time for expensive objective functions.

Choosing an optimisation method

For smooth deterministic objectives, quasi-Newton methods (e.g., "BFGS" or "L-BFGS-B" with box constraints) are often efficient when gradients are available or can be reliably approximated. For box-constrained problems, consider "L-BFGS-B" or the extended bounded solvers (e.g., "Rvmmin", "spg"). For noisy or stochastic objectives, heuristic/global methods (e.g., "AHR-ES") may be more appropriate.

Notes

"SANN" is included for compatibility with stats::optim(), but it is highly sensitive to tuning and often performs poorly on continuous problems under default settings. For noisy or rugged objective functions, "AHR-ES" is generally the recommended heuristic alternative within optim2().

Author

Ricardo Oliveros-Ramos

Examples

optim2(par=rep(NA, 5), fn=sphereN)
#> $par
#> [1] -0.003853539 -0.030986287  0.060781610 -0.040176383  0.060071570
#> 
#> $value
#> [1] 0.003254764
#> 
#> $counts
#> function gradient 
#>      505       NA 
#> 
#> $convergence
#> [1] 1
#> 
#> $message
#> NULL
#>