1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177

// Copyright 2018 Stefan Kroboth
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or
// http://opensource.org/licenses/MIT>, at your option. This file may not be
// copied, modified, or distributed except according to those terms.

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

use crate::prelude::*;
use serde::de::DeserializeOwned;
use serde::{Deserialize, Serialize};
use std::fmt::Debug;

/// BFGS method
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/bfgs.rs)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Serialize, Deserialize)]
pub struct BFGS<L, H> {
    /// Inverse Hessian
    inv_hessian: H,
    /// line search
    linesearch: L,
}

impl<L, H> BFGS<L, H> {
    /// Constructor
    pub fn new(init_inverse_hessian: H, linesearch: L) -> Self {
        BFGS {
            inv_hessian: init_inverse_hessian,
            linesearch,
        }
    }
}

impl<O, L, H> Solver<O> for BFGS<L, H>
where
    O: ArgminOp<Output = f64, Hessian = H>,
    O::Param: Debug
        + Default
        + ArgminSub<O::Param, O::Param>
        + ArgminDot<O::Param, f64>
        + ArgminDot<O::Param, O::Hessian>
        + ArgminScaledAdd<O::Param, f64, O::Param>
        + ArgminNorm<f64>
        + ArgminMul<f64, O::Param>,
    O::Hessian: Clone
        + Default
        + Debug
        + Serialize
        + DeserializeOwned
        + ArgminSub<O::Hessian, O::Hessian>
        + ArgminDot<O::Param, O::Param>
        + ArgminDot<O::Hessian, O::Hessian>
        + ArgminAdd<O::Hessian, O::Hessian>
        + ArgminMul<f64, O::Hessian>
        + ArgminTranspose
        + ArgminEye,
    L: Clone + ArgminLineSearch<O::Param> + Solver<OpWrapper<O>>,
{
    const NAME: &'static str = "BFGS";

    fn init(
        &mut self,
        op: &mut OpWrapper<O>,
        state: &IterState<O>,
    ) -> Result<Option<ArgminIterData<O>>, Error> {
        let param = state.get_param();
        let cost = op.apply(&param)?;
        let grad = op.gradient(&param)?;
        Ok(Some(
            ArgminIterData::new().param(param).cost(cost).grad(grad),
        ))
    }

    fn next_iter(
        &mut self,
        op: &mut OpWrapper<O>,
        state: &IterState<O>,
    ) -> Result<ArgminIterData<O>, Error> {
        let param = state.get_param();
        let cur_cost = state.get_cost();
        let prev_grad = state.get_grad().unwrap();
        // let prev_grad = if let Some(grad) = state.get_grad() {
        //     grad
        // } else {
        //     op.gradient(&param)?
        // };

        let p = self.inv_hessian.dot(&prev_grad).mul(&(-1.0));

        self.linesearch.set_search_direction(p);

        // Run solver
        let ArgminResult {
            operator: line_op,
            state:
                IterState {
                    param: xk1,
                    cost: next_cost,
                    ..
                },
        } = Executor::new(
            OpWrapper::new_from_op(&op),
            self.linesearch.clone(),
            param.clone(),
        )
        .grad(prev_grad.clone())
        .cost(cur_cost)
        .ctrlc(false)
        .run()?;

        // take care of function eval counts
        op.consume_op(line_op);

        let grad = op.gradient(&xk1)?;
        // let next_cost = op.apply(&xk1)?;

        let yk = grad.sub(&prev_grad);

        let sk = xk1.sub(&param);

        let yksk: f64 = yk.dot(&sk);
        let rhok = 1.0 / yksk;

        let e = self.inv_hessian.eye_like();
        let mat1: O::Hessian = sk.dot(&yk);
        let mat1 = mat1.mul(&rhok);

        let mat2 = mat1.clone().t();

        let tmp1 = e.sub(&mat1);
        let tmp2 = e.sub(&mat2);

        let sksk: O::Hessian = sk.dot(&sk);
        let sksk = sksk.mul(&rhok);

        // if state.get_iter() == 0 {
        //     let ykyk: f64 = yk.dot(&yk);
        //     self.inv_hessian = self.inv_hessian.eye_like().mul(&(yksk / ykyk));
        //     println!("{:?}", self.inv_hessian);
        // }

        self.inv_hessian = tmp1.dot(&self.inv_hessian.dot(&tmp2)).add(&sksk);

        Ok(ArgminIterData::new().param(xk1).cost(next_cost).grad(grad))
    }

    fn terminate(&mut self, state: &IterState<O>) -> TerminationReason {
        if state.get_grad().unwrap().norm() < std::f64::EPSILON.sqrt() {
            return TerminationReason::TargetPrecisionReached;
        }
        if (state.get_prev_cost() - state.get_cost()).abs() < std::f64::EPSILON {
            return TerminationReason::NoChangeInCost;
        }
        TerminationReason::NotTerminated
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::send_sync_test;
    use crate::solver::linesearch::MoreThuenteLineSearch;

    type Operator = MinimalNoOperator;

    send_sync_test!(bfgs, BFGS<Operator, MoreThuenteLineSearch<Operator>>);
}