Version:

Last Modified: March 15, 2017

Uses the downhill simplex method to determine a local minimum of a function of *n* independent variables.

Points at which the optimization process starts. These points form a simplex in *n* dimension.

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.

**Default: **No error

Accuracy of the minimum of the formula.

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

**Default: **1E-08

Local minimum in *n* dimension.

Function value at the local minimum.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

The downhill simplex method, also called the Nelder-Mead method, works without partial derivatives. The downhill simplex method consists of catching the minimum of the function *f*(*x*) with the help of simple geometrical bodies, specifically a simplex.

A simplex in 2D is a triangle; a simplex in 3D is a tetrahedron, and so on. You must have (*n* + 1) starting points, each of dimension *n*, forming the initial simplex. You must enter only one point of these (*n* + 1) starting points. The (*n* + 1) dimensional simplex is constructed automatically.

For the function defined by equation *f*(*x*, *y*) = *x*^{2} + *y*^{2}, you must enter two numbers, describing exactly one point in 2D. The method generates a new simplex by some elementary operations such as reflections, expansions, and contractions. In the end, the minimum is concentrated in a very small simplex.

To find the simplex sequence tending to the minimum (0, 0) of the preceding function, enter the following values on the panel:

formula |
[x*x + y*y] |

start |
[3.2, 1] |

The following illustration shows the simplex sequence tending to the minimum (0, 0) of the preceding function.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices