# direct1d: Univariate Global Optimization

### Description

Implementation of the DIRECT global optimization algorithm in the one-dimensional case.

### Usage

 `1` ```direct1d(f, a, b, maxiter = 20, ...) ```

### Arguments

 `f` function to be minimized. `a, b` end points of the interval, `a

### Details

The DIRECT algorithm for the one-dimensional case is directly derived from Shubert's algorithm. Instead of computing the function at the endpoints of the interval, it is computed at the midpoint. Intervals ar split in three parts, sparing one function evaluation.

### Value

List with components `xmin` and `fmin`, the minimum found so far and its function value.

### Note

The subroutine for finding the set of optimal subintervals is slow and has to be intelligently refitted.

### References

Jones, D. R., C. D. Perttunen, and B. E. Stuckman (1993). Lipschitzian Optimization Without the Lipschitz Constant. Journal of Optimization Theory and Application, Vol. 79. No. 1, pp. 157ff.

Finkel, D., and C. Kelley (2006). Additive Scaling and the DIRECT Algorithm. Journal of Global Optimization, Vol. 36, No. 4, pp. 597–608.

`findmins`, `dfoptim::direct`

### Examples

 ```1 2 3 4 5 6 7 8``` ```f <- function(x) sin(10*pi*x) + 0.5*(x-0.5)^2 a <- 0; b <- 1 direct1d(f, 0, 1, maxiter = 20) # \$xmin: 0.5499493794 (error: 3.5e-6) # \$fmin: -0.9987512652 ## Not run: ezplot(f, a, b, 1000) ## End(Not run) ```

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