Struct argmin::solver::newton::newton_cg::NewtonCG

pub struct NewtonCG<'a, O> where
    O: 'a + ArgminOp<Output = f64>,
    <O as ArgminOp>::Param: ArgminSub<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminAdd<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminDot<<O as ArgminOp>::Param, f64> + ArgminScaledAdd<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param> + ArgminMul<f64, <O as ArgminOp>::Param> + ArgminZero + ArgminNorm<f64>,
    <O as ArgminOp>::Hessian: ArgminInv<<O as ArgminOp>::Hessian> + ArgminDot<<O as ArgminOp>::Param, <O as ArgminOp>::Param>,  { /* fields omitted */ }

The Newton-CG method (also called truncated Newton method) uses a modified CG to solve the Newton equations approximately. After a search direction is found, a line search is performed.

Example

use argmin::prelude::*;
use argmin::solver::newton::NewtonCG;
use ndarray::{Array, Array1, Array2};

// Define cost function
let cost = MyProblem {};

// Define initial parameter vector
let init_param: Array1<f64> = Array1::from_vec(vec![-1.2, 1.0]);

// Set up solver
let mut solver = NewtonCG::new(cost, init_param);

// Set maximum number of iterations
solver.set_max_iters(20);

// Attach a logger
solver.add_logger(ArgminSlogLogger::term());

// Run solver
solver.run()?;

// Wait a second (lets the logger flush everything before printing again)
std::thread::sleep(std::time::Duration::from_secs(1));

// Print result
println!("{:?}", solver.result());

References:

[0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization. Springer. ISBN 0-387-30303-0.

Methods

impl<'a, O> NewtonCG<'a, O> where
    O: 'a + ArgminOp<Output = f64>,
    <O as ArgminOp>::Param: ArgminSub<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminAdd<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminDot<<O as ArgminOp>::Param, f64> + ArgminScaledAdd<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param> + ArgminMul<f64, <O as ArgminOp>::Param> + ArgminZero + ArgminNorm<f64>,
    <O as ArgminOp>::Hessian: ArgminInv<<O as ArgminOp>::Hessian> + ArgminDot<<O as ArgminOp>::Param, <O as ArgminOp>::Param>, 

pub fn new(cost_function: O, init_param: <O as ArgminOp>::Param) -> Self

Constructor

pub fn set_linesearch(
    &mut self,
    linesearch: Box<dyn ArgminLineSearch<Param = <O as ArgminOp>::Param, Output = <O as ArgminOp>::Output, Hessian = <O as ArgminOp>::Hessian> + 'a>
) -> &mut Self

Specify line search method

pub fn set_curvature_threshold(&mut self, threshold: f64) -> &mut Self

Set curvature threshold

Trait Implementations

impl<'a, O> ArgminSolver for NewtonCG<'a, O> where
    O: 'a + ArgminOp<Output = f64>,
    <O as ArgminOp>::Param: ArgminSub<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminAdd<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminDot<<O as ArgminOp>::Param, f64> + ArgminScaledAdd<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param> + ArgminMul<f64, <O as ArgminOp>::Param> + ArgminZero + ArgminNorm<f64>,
    <O as ArgminOp>::Hessian: ArgminInv<<O as ArgminOp>::Hessian> + ArgminDot<<O as ArgminOp>::Param, <O as ArgminOp>::Param>, 

fn run(&mut self) -> Result<ArgminResult<Self::Param>, Error>

Run the optimization algorithm

fn run_fast(&mut self) -> Result<ArgminResult<Self::Param>, Error>

Run the essential parts of the optimization algorithm (no logging, no Ctrl-C handling)

fn apply(&mut self, param: &Self::Param) -> Result<Self::Output, Error>

Applies the cost function or operator to a parameter vector param. Returns an Err if apply of ArgminOperator is not implemented.

fn gradient(&mut self, param: &Self::Param) -> Result<Self::Param, Error>

Computes the gradient at parameter param. Returns an Err if gradient of ArgminOperator is not implemented.

fn hessian(&mut self, param: &Self::Param) -> Result<Self::Hessian, Error>

Computes the Hessian at parameter param. Returns an Err if hessian of ArgminOperator is not implemented.

fn cur_param(&self) -> Self::Param

Returns the current parameter vector.

fn cur_grad(&self) -> Self::Param

Returns the most recently stored gradient.

fn cur_hessian(&self) -> Self::Hessian

Returns the most recently stored Hessian.

fn set_cur_param(&mut self, param: Self::Param)

Sets the current parameter to param.

fn set_cur_grad(&mut self, grad: Self::Param)

Sets the current gradient to grad.

fn set_cur_hessian(&mut self, hessian: Self::Hessian)

Sets the current Hessian to hessian.

fn set_best_param(&mut self, param: Self::Param)

Sets the best parameter vector to param.

fn modify(&self, param: &Self::Param, factor: f64) -> Result<Self::Param, Error>

Modify the parameter vector by calling the modify method of the trait ArgminOperator. Will return an Err if modify is not implemented.

fn result(&self) -> ArgminResult<Self::Param>

Returns the result of the optimization.

fn set_max_iters(&mut self, iters: u64)

Sets the maximum number of iterations to iters.

fn max_iters(&self) -> u64

Returns the maximum number of iterations.

fn increment_iter(&mut self)

Increments the iteration counter.

fn cur_iter(&self) -> u64

Returns the current number of iterations.

fn cur_cost(&self) -> f64

Returns the most recently stored cost function value.

fn set_cur_cost(&mut self, cost: f64)

Sets the current cost function value to cost

fn best_cost(&self) -> f64

Returns the best cost function value obtained so far.

fn set_best_cost(&mut self, cost: f64)

Sets the best cost function value.

fn set_target_cost(&mut self, cost: f64)

Sets the target cost function value to cost. The optimization algorithm will be terminated when this limit is reached.

fn increment_cost_func_count(&mut self)

Increments the counter for the computations of the cost function by 1.

fn increase_cost_func_count(&mut self, count: u64)

Increases the counter for the computations of the cost function by count.

fn cost_func_count(&self) -> u64

Returns the current value of the counter for the computations of the cost function.

fn increment_grad_func_count(&mut self)

Increments the counter for the computations of the gradient by 1.

fn increase_grad_func_count(&mut self, count: u64)

Increases the counter for the computations of the gradient by count.

fn grad_func_count(&self) -> u64

Returns the current value of the counter for the computations of the gradient.

fn increment_hessian_func_count(&mut self)

Increments the counter for the computations of the Hessian by 1.

fn increase_hessian_func_count(&mut self, count: u64)

Increases the counter for the computations of the Hessian by count.

fn hessian_func_count(&self) -> u64

Returns the current value of the counter for the computations of the Hessian.

fn add_logger(&mut self, logger: Arc<dyn ArgminLog>)

Attaches a logger which implements ArgminLog to the solver.

fn add_writer(&mut self, writer: Arc<dyn ArgminWrite<Param = Self::Param>>)

Attaches a writer which implements ArgminWrite to the solver.

fn set_termination_reason(&mut self, reason: TerminationReason)

Sets the TerminationReason

fn terminate(&mut self) -> TerminationReason

Checks whether any of the conditions to terminate is true and terminates the algorithm.

fn base_reset(&mut self)

Resets the base field to it's initial conditions. This is helpful for implementing a solver which is initialized once, but called several times. It is recommended to only call this method inside the init function of ArgminNextIter.

impl<'a, O> ArgminIter for NewtonCG<'a, O> where
    O: 'a + ArgminOp<Output = f64>,
    <O as ArgminOp>::Param: ArgminSub<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminAdd<<O as ArgminOp>::Param, <O as ArgminOp>::Param> + ArgminDot<<O as ArgminOp>::Param, f64> + ArgminScaledAdd<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param> + ArgminMul<f64, <O as ArgminOp>::Param> + ArgminZero + ArgminNorm<f64>,
    <O as ArgminOp>::Hessian: ArgminInv<<O as ArgminOp>::Hessian> + ArgminDot<<O as ArgminOp>::Param, <O as ArgminOp>::Param>, 

type Param = <O as ArgminOp>::Param

Parameter vectors

type Output = <O as ArgminOp>::Output

Output of the operator

type Hessian = <O as ArgminOp>::Hessian

Hessian

fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error>

Computes one iteration of the algorithm.

fn init(&mut self) -> Result<(), Error>

Initializes the algorithm