Struct HagerZhangLineSearch

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

Hager-Zhang line search

The Hager-Zhang line search is a method to find a step length which obeys the strong Wolfe conditions.

Requirements on the optimization problem

The optimization problem is required to implement CostFunction and Gradient.

Reference

William W. Hager and Hongchao Zhang. “A new conjugate gradient method with guaranteed descent and an efficient line search.” SIAM J. Optim. 16(1), 2006, 170-192. DOI: https://doi.org/10.1137/030601880

Implementations

impl<P, G, F> HagerZhangLineSearch<P, G, F>

where P: ArgminScaledAdd<G, F, P>, G: ArgminDot<G, F>, F: ArgminFloat,

pub fn new() -> Self

Construct a new instance of HagerZhangLineSearch

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> = HagerZhangLineSearch::new();

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

Set delta and sigma.

Delta defaults to 0.1 and must be in (0, 1). Sigma defaults to 0.9 and must be in [delta, 1).

Delta and Sigma correspond to the constants c1 and c2 of the strong Wolfe conditions, respectively.

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_delta_sigma(0.2, 0.8)?;

pub fn with_epsilon(self, epsilon: F) -> Result<Self, Error>

Set epsilon

Used in the approximate strong Wolfe condition.

Must be non-negative and defaults to 1e-6.

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_epsilon(1e-8)?;

pub fn with_theta(self, theta: F) -> Result<Self, Error>

Set theta

Used in the update rules when the potential intervals [a, c] or [c, b] violate the opposite slope condition.

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

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_theta(0.4)?;

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

Set gamma

Determines when a bisection step is performed.

Must be in (0, 1) and defaults to 0.66.

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_gamma(0.7)?;

pub fn with_eta(self, eta: F) -> Result<Self, Error>

Set eta

Used in the lower bound for beta_k^N.

Must be larger than zero and defaults to 0.01.

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_eta(0.02)?;

pub fn with_bounds(self, step_min: F, step_max: F) -> Result<Self, Error>

Set lower and upper bound of step

Defaults to a minimum step length of EPSILON and a maximum step length of 1e5.

The chosen values must satisfy 0 <= step_min < step_max.

Example

let hzls: HagerZhangLineSearch<Vec<f64>, Vec<f64>, f64> =
    HagerZhangLineSearch::new().with_bounds(1e-3, 1.0)?;

Trait Implementations

impl<P: Clone, G: Clone, F: Clone> Clone for HagerZhangLineSearch<P, G, F>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<P, G, F> Default for HagerZhangLineSearch<P, G, F>

where P: ArgminScaledAdd<G, F, P>, G: ArgminDot<G, F>, F: ArgminFloat,

fn default() -> Self

Returns the “default value” for a type.

impl<'de, P, G, F> Deserialize<'de> for HagerZhangLineSearch<P, G, F>

where P: Deserialize<'de>, G: 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, G, F> LineSearch<G, F> for HagerZhangLineSearch<P, G, F>

fn search_direction(&mut self, search_direction: G)

Set search direction

fn initial_step_length(&mut self, alpha: F) -> Result<(), Error>

Set initial alpha value

impl<P, G, F> Serialize for HagerZhangLineSearch<P, G, F>

where P: Serialize, G: 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<P, G, O, F> Solver<O, IterState<P, G, (), (), (), F>> for HagerZhangLineSearch<P, G, F>

where O: CostFunction<Param = P, Output = F> + Gradient<Param = P, Gradient = G>, P: Clone + ArgminDot<G, F> + ArgminScaledAdd<G, F, P>, G: Clone + ArgminDot<G, F>, F: ArgminFloat,

fn name(&self) -> &str

Name of the solver. Mainly used in Observers.

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

Initializes the algorithm.

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

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

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

Checks whether basic termination reasons apply.