Struct argmin::solver::neldermead::NelderMead

pub struct NelderMead<P, F> { /* private fields */ }

Nelder-Mead method

The Nelder-Mead method a heuristic search method for nonlinear optimization problems which does not require derivatives.

The method is based on simplices which consist of n+1 vertices for an optimization problem with n dimensions. The function to be optimized is evaluated at all vertices. Based on these cost function values the behaviour of the cost function is extrapolated in order to find the next point to be evaluated.

The following actions are possible:

1. Reflection (Parameter alpha, defaults to 1, configurable via with_alpha)
2. Expansion (Parameter gamma, defaults to 2, configurable via with_gamma)
3. Contraction inside or outside (Parameter rho, defaults to 0.5, configurable via with_rho)
4. Shrink (Parameter sigma, defaults to 0.5, configurable via with_sigma)

Requirements on the optimization problem

The optimization problem is required to implement CostFunction.

References

https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

http://www.scholarpedia.org/article/Nelder-Mead_algorithm#Simplex_transformation_algorithm

Implementations

impl<P, F> NelderMead<P, F> where
    P: Clone + ArgminAdd<P, P> + ArgminSub<P, P> + ArgminMul<F, P>,
    F: ArgminFloat, 

pub fn new(params: Vec<P>) -> Self

Construct a new instance of NelderMead

Takes a vector of parameter vectors. The number of parameter vectors must be n + 1 where n is the number of optimization parameters.

Example

let nm: NelderMead<Vec<f64>, f64> = NelderMead::new(vec_of_parameters);

pub fn with_sd_tolerance(self, tol: F) -> Result<Self, Error>

Set sample standard deviation tolerance

Must be non-negative and defaults to EPSILON.

Example

let nm: NelderMead<Vec<f64>, f64> =
    NelderMead::new(vec_of_parameters).with_sd_tolerance(1e-6)?;

pub fn with_alpha(self, alpha: F) -> Result<Self, Error>

Set alpha parameter for reflection

Must be larger than 0 and defaults to 1.

Example

let nm: NelderMead<Vec<f64>, f64> =
    NelderMead::new(vec_of_parameters).with_alpha(0.9)?;

pub fn with_gamma(self, gamma: F) -> Result<Self, Error>

Set gamma for expansion

Must be larger than 1 and defaults to 2.

Example

let nm: NelderMead<Vec<f64>, f64> =
    NelderMead::new(vec_of_parameters).with_gamma(1.9)?;

pub fn with_rho(self, rho: F) -> Result<Self, Error>

Set rho for contraction

Must be in (0, 0.5] and defaults to 0.5.

Example

let nm: NelderMead<Vec<f64>, f64> =
    NelderMead::new(vec_of_parameters).with_rho(0.4)?;

pub fn with_sigma(self, sigma: F) -> Result<Self, Error>

Set sigma for shrinking

Must be in (0, 1] and defaults to 0.5.

Example

let nm: NelderMead<Vec<f64>, f64> =
    NelderMead::new(vec_of_parameters).with_sigma(0.4)?;

Trait Implementations

impl<P: Clone, F: Clone> Clone for NelderMead<P, F>

fn clone(&self) -> NelderMead<P, F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<'de, P, F> Deserialize<'de> for NelderMead<P, F> where
    P: Deserialize<'de>,
    F: Deserialize<'de>, 

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<P, F> Serialize for NelderMead<P, F> where
    P: Serialize,
    F: Serialize, 

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

impl<O, P, F> Solver<O, IterState<P, (), (), (), F>> for NelderMead<P, F> where
    O: CostFunction<Param = P, Output = F>,
    P: Clone + SerializeAlias + ArgminSub<P, P> + ArgminAdd<P, P> + ArgminMul<F, P>,
    F: ArgminFloat + Sum<F>, 

const NAME: &'static str = "Nelder-Mead method"

Name of the solver. Mainly used in Observers.

fn init(
    &mut self,
    problem: &mut Problem<O>,
    state: IterState<P, (), (), (), F>
) -> Result<(IterState<P, (), (), (), F>, Option<KV>), Error>

Initializes the algorithm.

fn next_iter(
    &mut self,
    problem: &mut Problem<O>,
    state: IterState<P, (), (), (), F>
) -> Result<(IterState<P, (), (), (), F>, Option<KV>), Error>

Computes a single iteration of the algorithm and has access to the optimization problem definition and the internal state of the solver. Returns an updated state and optionally a KV which holds key-value pairs used in Observers.

fn terminate(
    &mut self,
    _state: &IterState<P, (), (), (), F>
) -> TerminationReason

Used to implement stopping criteria, in particular criteria which are not covered by (terminate_internal.

fn terminate_internal(&mut self, state: &I) -> TerminationReason

Checks whether basic termination reasons apply.