Nelder-Mead

class pints.NelderMead(x0, sigma0=None, boundaries=None)

Nelder-Mead downhill simplex method.

Implementation of the classical algorithm by [1], following the presentation in Algorithm 8.1 of [2].

This is a deterministic local optimiser. In most update steps it performs either 1 evaluation, or 2 sequential evaluations, so that it will not typically benefit from parallelisation.

Generates a “simplex” of n + 1 samples around a given starting point, and evaluates their scores. Next, each iteration consists of a sequence of operations, typically the worst sample y_worst is replaced with a new point:

y_new = mu + delta * (mu - y_worst)
mu = (1 / n) * sum(y), y != y_worst

where delta has one of four values, depending on the type of operation:

• Reflection (delta = 1)
• Expansion (delta = 2)
• Inside contraction (delta = -0.5)
• Outside contraction (delta = 0.5)

Note that the delta values here are common choices, but not the only valid choices.

A fifth type of iteration called a “shrink” is occasionally performed, in which all samples except the best sample y_best are replaced:

y_i_new = y_best + ys * (y_i - y_best)

where ys is a parameter (typically ys = 0.5).

The initialisation of the initial simplex was copied from [3].

References

[1]	A simplex method for function minimization Nelder, Mead 1965, Computer Journal https://doi.org/10.1093/comjnl/7.4.308

[2]	Introduction to derivative-free optimization Andrew R. Conn, Katya Scheinberg, Luis N. Vicente 2009, First edition. ISBN 978-0-098716-68-9 https://doi.org/10.1137/1.9780898718768

[3]	SciPy on GitHub https://github.com/scipy/scipy/

ask()

See: pints.Optimiser.ask().

fbest()

See: pints.Optimiser.fbest().

n_hyper_parameters()

Returns the number of hyper-parameters for this method (see TunableMethod).

name()

See: pints.Optimiser.name().

needs_sensitivities()

Returns True if this methods needs sensitivities to be passed in to tell along with the evaluated error.

running()

See: pints.Optimiser.running().

set_hyper_parameters(x)

Sets the hyper-parameters for the method with the given vector of values (see TunableMethod).

Parameters:x – An array of length n_hyper_parameters used to set the hyper-parameters.

stop()

See: pints.Optimiser.stop().

tell(fx)

See: pints.Optimiser.tell().

xbest()

See: pints.Optimiser.xbest().