stogo function

Stochastic Global Optimization

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 using a gradient-based local-search algorithm (a BFGS variant), optionally including some randomness.

stogo(
  x0,
  fn,
  gr = NULL,
  lower = NULL,
  upper = NULL,
  maxeval = 10000,
  xtol_rel = 1e-06,
  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 be shown.
• ...: additional arguments passed to the function.

Returns

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.

Note

Only bounds-constrained problems are supported by this algorithm.

Examples

## Rosenbrock Banana objective function

rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2}

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

## The function as written above has a minimum of 0 at (1, 1)

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

References

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

Author(s)

Hans W. Borchers