optimInterface: Optimization Interface (continuous, bounded)

Description

This function is an interface fashioned like the optim function. Unlike optim, it collects a set of bound-constrained optimization algorithms with local as well as global approaches. It is, e.g., used in the CEGO package to solve the optimization problem that occurs during parameter estimation in the Kriging model (based on Maximum Likelihood Estimation). Note that this function is NOT applicable to combinatorial optimization problems.

Usage

optimInterface(x, fun, lower = -Inf, upper = Inf, control = list(), ...)

Value

This function returns a list with:

xbest: parameters of the found solution
ybest: target function value of the found solution
count: number of evaluations of fun

Arguments

x: is a point (vector) in the decision space of fun
fun: is the target function of type y = f(x, ...)
lower: is a vector that defines the lower boundary of search space
upper: is a vector that defines the upper boundary of search space
control: is a list of additional settings. See details.
...: additional parameters to be passed on to fun

Details

The control list contains:

funEvals: stopping criterion, number of evaluations allowed for fun (defaults to 100)
reltol: stopping criterion, relative tolerance (default: 1e-6)
factr: stopping criterion, specifying relative tolerance parameter factr for the L-BFGS-B method in the optim function (default: 1e10)
popsize: population size or number of particles (default: 10*dimension, where dimension is derived from the length of the vector lower).
restarts: whether to perform restarts (Default: TRUE). Restarts will only be performed if some of the evaluation budget is left once the algorithm stopped due to some stopping criterion (e.g., reltol).
method: will be used to choose the optimization method from the following list: "L-BFGS-B" - BFGS quasi-Newton: stats Package optim function
"nlminb" - box-constrained optimization using PORT routines: stats Package nlminb function
"DEoptim" - Differential Evolution implementation: DEoptim Package
Additionally to the above methods, several methods from the package nloptr can be chosen. The complete list of suitable nlopt methods (non-gradient, bound constraints) is:
"NLOPT_GN_DIRECT","NLOPT_GN_DIRECT_L","NLOPT_GN_DIRECT_L_RAND", "NLOPT_GN_DIRECT_NOSCAL","NLOPT_GN_DIRECT_L_NOSCAL","NLOPT_GN_DIRECT_L_RAND_NOSCAL", "NLOPT_GN_ORIG_DIRECT","NLOPT_GN_ORIG_DIRECT_L","NLOPT_LN_PRAXIS", "NLOPT_GN_CRS2_LM","NLOPT_LN_COBYLA", "NLOPT_LN_NELDERMEAD","NLOPT_LN_SBPLX","NLOPT_LN_BOBYQA","NLOPT_GN_ISRES"

All of the above methods use bound constraints. For references and details on the specific methods, please check the documentation of the packages that provide them.