nloptr (version 1.0.0)

cobyla: Constrained Optimization by Linear Approximations

Description

COBYLA is an algorithm for derivative-free optimization with nonlinear inequality and equality constraints (but see below).

Usage

cobyla(x0, fn, lower = NULL, upper = NULL, hin = NULL,
        nl.info = FALSE, control = list(), ...)

Arguments

x0
starting point for searching the optimum.
fn
objective function that is to be minimized.
lower, upper
lower and upper bound constraints.
hin
function defining the inequality constraints, that is hin>=0 for all components.
nl.info
logical; shall the original NLopt info been shown.
control
list of options, see nl.opts for help.
...
additional arguments passed to the function.

Value

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

Details

It constructs successive linear approximations of the objective function and constraints via a simplex of n+1 points (in n dimensions), and optimizes these approximations in a trust region at each step.

COBYLA supports equality constraints by transforming them into two inequality constraints. As this does not give full satisfaction with the implementation in NLOPT, it has not been made available here.

References

M. J. D. Powell, ``A direct search optimization method that models the objective and constraint functions by linear interpolation,'' in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. Hennart (Kluwer Academic: Dordrecht, 1994), p. 51-67.

See Also

bobyqa, newuoa

Examples

Run this code
### Solve Hock-Schittkowski no. 100
x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1)
fn.hs100 <- function(x) {
    (x[1]-10)^2 + 5*(x[2]-12)^2 + x[3]^4 + 3*(x[4]-11)^2 + 10*x[5]^6 +
                  7*x[6]^2 + x[7]^4 - 4*x[6]*x[7] - 10*x[6] - 8*x[7]
}
hin.hs100 <- function(x) {
    h <- numeric(4)
    h[1] <- 127 - 2*x[1]^2 - 3*x[2]^4 - x[3] - 4*x[4]^2 - 5*x[5]
    h[2] <- 282 - 7*x[1] - 3*x[2] - 10*x[3]^2 - x[4] + x[5]
    h[3] <- 196 - 23*x[1] - x[2]^2 - 6*x[6]^2 + 8*x[7]
    h[4] <- -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6]	+11*x[7]
    return(h)
}

S <- cobyla(x0.hs100, fn.hs100, hin = hin.hs100,
            nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 2000))
## Optimal value of objective function:  680.630057374431

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