# Four-Dimensional Golden Search

## Abstract

The Golden search technique is a method to search a multiple-dimension space to find the minimum. It basically subdivides the possible ranges of parameters until it brackets, to within an arbitrarily small distance, the minimum. It has the advantages that (1) the function to be minimized can be non-linear, (2) it does not require derivatives of the function, (3) the convergence criterion does not depend on the magnitude of the function. Thus, if the function is a goodness of fit parameter such as chi-square, the convergence does not depend on the noise being correctly estimated or the function correctly following the chi-square statistic. And, (4) the convergence criterion does not depend on the shape of the function. Thus, long shallow surfaces can be searched without the problem of premature convergence. As with many methods, the Golden search technique can be confused by surfaces with multiple minima.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1171678

- Report Number(s):
- LA-UR-15-21424

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS

### Citation Formats

```
Fenimore, Edward E.
```*Four-Dimensional Golden Search*. United States: N. p., 2015.
Web. doi:10.2172/1171678.

```
Fenimore, Edward E.
```*Four-Dimensional Golden Search*. United States. doi:10.2172/1171678.

```
Fenimore, Edward E. Wed .
"Four-Dimensional Golden Search". United States.
doi:10.2172/1171678. https://www.osti.gov/servlets/purl/1171678.
```

```
@article{osti_1171678,
```

title = {Four-Dimensional Golden Search},

author = {Fenimore, Edward E.},

abstractNote = {The Golden search technique is a method to search a multiple-dimension space to find the minimum. It basically subdivides the possible ranges of parameters until it brackets, to within an arbitrarily small distance, the minimum. It has the advantages that (1) the function to be minimized can be non-linear, (2) it does not require derivatives of the function, (3) the convergence criterion does not depend on the magnitude of the function. Thus, if the function is a goodness of fit parameter such as chi-square, the convergence does not depend on the noise being correctly estimated or the function correctly following the chi-square statistic. And, (4) the convergence criterion does not depend on the shape of the function. Thus, long shallow surfaces can be searched without the problem of premature convergence. As with many methods, the Golden search technique can be confused by surfaces with multiple minima.},

doi = {10.2172/1171678},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Feb 25 00:00:00 EST 2015},

month = {Wed Feb 25 00:00:00 EST 2015}

}