nloptr (version 1.0.0)

stogo: Stochastic Global Optimization

Description

StoGO is a global optimization algorithm that works by systematically dividing the search space into smaller hyper-rectangles.

Usage

stogo(x0, fn, gr = NULL, lower = NULL, upper = NULL,
      maxeval = 10000, xtol_rel = 1e-6, randomized = FALSE,
      nl.info = FALSE, ...)

Arguments

x0

initial point for searching the optimum.

fn

objective function that is to be minimized.

gr

optional gradient of the objective function.

lower, upper

lower and upper bound constraints.

maxeval

maximum number of function evaluations.

xtol_rel

stopping criterion for relative change reached.

randomized

logical; shall a randomizing variant be used?

nl.info

logical; shall the original NLopt info been shown.

...

additional arguments passed to the function.

Value

• List with components:
• par
  the optimal solution found so far.
• value
  the function value corresponding to par.
• iter
  number of (outer) iterations, see maxeval.
• convergence
  integer code indicating successful completion (> 0) or a possible error number (< 0).
• message
  character string produced by NLopt and giving additional information.

Details

StoGO is a global optimization algorithm that works by systematically dividing the search space (which must be bound-constrained) into smaller hyper-rectangles via a branch-and-bound technique, and searching them by a gradient-based local-search algorithm (a BFGS variant), optionally including some randomness.

References

S. Zertchaninov and K. Madsen, ``A C++ Programme for Global Optimization,'' IMM-REP-1998-04, Department of Mathematical Modelling, Technical University of Denmark.

Examples

### Rosenbrock Banana objective function
fn <- function(x)
    return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 )

x0 <- c( -1.2, 1 )
lb <- c( -3, -3 )
ub <- c(  3,  3 )

stogo(x0 = x0, fn = fn, lower = lb, upper = ub)