emmy.numerical.multimin.nelder-mead
nelder-meadclj/s
(nelder-mead func x0 {:keys [callback] :as opts})Find the minimum of the function f: R^n -> R, given an initial point q ∈ R^n. Supports the following optional keyword arguments:
:callback if supplied, the supplied fn will be invoked with iteration count,
the values of X and the value of f(X) at each intermediate point of
evaluation.
:info? if true, wraps the result with evaluation information.
:adaptive? if true, the Nelder-Mead parameters for contraction, expansion,
reflection and shrinking will be set adaptively, as functions of the number of
dimensions. If false they stay constant.
:alpha sets the reflection coefficient used for each step of Nelder-Mead.
:beta sets the expansion coefficient used for each step of Nelder-Mead.
:gamma sets the contraction coefficient used for each step of Nelder-Mead.
:sigma sets the shrink coefficient used for each step of Nelder-Mead.
:maxiter Maximum number of iterations allowed for the minimizer. Defaults to
200*dimension.
:maxfun Maximum number of times the function can be evaluated before exiting.
Defaults to 200*dimension.
:simplex-tolerance When the absolute value of the max difference between the
best point and any point in the simplex falls below this tolerance, the
minimizer stops. Defaults to 1e-4.
:fn-tolerance When the absolute value of the max difference between the best
point's function value and the fn value of any point in the simplex falls
below this tolerance, the minimizer stops. Defaults to 1e-4.
:zero-delta controls the value to which 0 entries in the initial vector are
set during initial simplex generation. Defaults to 0.00025.
:nonzero-delta factor by which entries in the initial vector are perturbed to
generate the initial simplex. Defaults to 0.05.
See Gao, F. and Han, L. Implementing the Nelder-Mead simplex algorithm with adaptive parameters. 2012. Computational Optimization and Applications. 51:1, pp. 259-277 I gratefully acknowledge the Python implementation in SciPy which I have imitated here.
Find the minimum of the function f: R^n -> R, given an initial point q ∈ R^n.
Supports the following optional keyword arguments:
`:callback` if supplied, the supplied fn will be invoked with iteration count,
the values of X and the value of f(X) at each intermediate point of
evaluation.
`:info?` if true, wraps the result with evaluation information.
`:adaptive?` if true, the Nelder-Mead parameters for contraction, expansion,
reflection and shrinking will be set adaptively, as functions of the number of
dimensions. If false they stay constant.
`:alpha` sets the reflection coefficient used for each step of Nelder-Mead.
`:beta` sets the expansion coefficient used for each step of Nelder-Mead.
`:gamma` sets the contraction coefficient used for each step of Nelder-Mead.
`:sigma` sets the shrink coefficient used for each step of Nelder-Mead.
`:maxiter` Maximum number of iterations allowed for the minimizer. Defaults to
200*dimension.
`:maxfun` Maximum number of times the function can be evaluated before exiting.
Defaults to 200*dimension.
`:simplex-tolerance` When the absolute value of the max difference between the
best point and any point in the simplex falls below this tolerance, the
minimizer stops. Defaults to 1e-4.
`:fn-tolerance` When the absolute value of the max difference between the best
point's function value and the fn value of any point in the simplex falls
below this tolerance, the minimizer stops. Defaults to 1e-4.
`:zero-delta` controls the value to which 0 entries in the initial vector are
set during initial simplex generation. Defaults to 0.00025.
`:nonzero-delta` factor by which entries in the initial vector are perturbed to
generate the initial simplex. Defaults to 0.05.
See Gao, F. and Han, L.
Implementing the Nelder-Mead simplex algorithm with adaptive
parameters. 2012. Computational Optimization and Applications.
51:1, pp. 259-277
I gratefully acknowledge the [Python implementation in
SciPy](https://github.com/scipy/scipy/blob/589c9afe41774ee96ec121f1867361146add8276/scipy/optimize/optimize.py#L556:5)
which I have imitated here.
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