Nelder-Mead Simplex with Bounded Variables
Version
1.0
Description
Nelder-Mead Simplex is a non-gradient based algorithm to solve unconstrained
optimization problems. This implementation supports simple bounds
on design variables. Nelder-Mead uses a simplex that consists of N+1
vertices in N dimensions. Initially a small simplex is generated around
the initial design. The object function values of the N+1 points are
compared, and the worst design is replaced by a point reflected through
the centroid of the remaining N points. If the new design is no better
than the original design, the reflection step is reduced. If the new
design is better than the best design, the reflection step is increased.
This iteration continues until the size of the simplex becomes smaller
than tolerance.
References
- "A simplex method for function minimization," Nelder, J. A., Mead, R., Computer Journal 7, pp.308-313.
- See also Nelder Mead Method
Control Parameters
| Name | Default Value | Description |
|---|---|---|
| MaxIterations | 1000 | Maximum number of iterations the algorithm will run. This option must have a positive integer value. |
| Size | 0.05 | The option specifies the size of the initial simplex. Size should have a value greater than 0. |
| Tolerance | 0.0001 | The algorithm will terminate when the size of the simplex falls below this threshold value. Option must have a value greater than 0. |