# Find a Minimum 1D (Golden Section) (G Dataflow)

Determines a local minimum of a given 1D function with the help of a bracketing of the minimum. This node uses the golden section search method.  ## objective function

Formula that defines the objective function. The formula must contain one valid variable.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores. ## a

Left point of the bracketing interval.

Default: 0 ## b

Middle point of the bracketing interval.

Default: 0 ## c

Right point of the bracketing interval.

Default: 0 ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## accuracy

Accuracy of the minimum of the objective function.

The node stops running if the difference between two consecutive approximations is equal to or less than the value of accuracy.

Default: 1E-08 ## minimum

Local minimum of the objective function. ## f(minimum)

Value of the objective function at minimum. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## How the Golden Section Search Method Finds a Local Minimum

A bracketing triplet (a, b, c) of a 1D continuous function f is a combination of three points with f(a) > f(b) and f(c) > f(b). This guarantees the existence of a local minimum of f in the interval (a, c).

Beginning with a bracketing triplet (a, b, c), the golden section search method determines a new bracketing triplet with a considerably smaller expansion. Repeating this scheme often yields a good approximation of the local minimum. The following equation essentially calculates the new bracketing point.

$|\frac{x-b}{c-a}|=\left(\sqrt{5}-2\right)$

The following figure shows the relationship between a, b, c and f(a), f(b), f(c). Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application