venny/bin/fmin/line-search.js

Declarative Venn diagrams

import { dot, weightedSum } from './blas1';
/// searches along line 'pk' for a point that satifies the wolfe conditions
/// See 'Numerical Optimization' by Nocedal and Wright p59-60
/// f : objective function
/// pk : search direction
/// current: object containing current gradient/loss
/// next: output: contains next gradient/loss
/// returns a: step size taken
export function wolfeLineSearch(f, pk, current, next, ain, c1in, c2in) {
    const phi0 = current.fx, phiPrime0 = dot(current.fxprime, pk);
    let phi = phi0, phi_old = phi0, phiPrime = phiPrime0, a0 = 0;
    let a = ain || 1;
    const c1 = c1in || 1e-6;
    const c2 = c2in || 0.1;
    const zoom = (a_lo, a_high, phi_lo) => {
        for (let iteration = 0; iteration < 16; ++iteration) {
            a = (a_lo + a_high) / 2;
            weightedSum(next.x, 1.0, current.x, a, pk);
            phi = next.fx = f(next.x, next.fxprime);
            phiPrime = dot(next.fxprime, pk);
            if ((phi > (phi0 + c1 * a * phiPrime0)) ||
                (phi >= phi_lo)) {
                a_high = a;
            }
            else {
                if (Math.abs(phiPrime) <= -c2 * phiPrime0) {
                    return a;
                }
                if (phiPrime * (a_high - a_lo) >= 0) {
                    a_high = a_lo;
                }
                a_lo = a;
                phi_lo = phi;
            }
        }
        return 0;
    };
    for (let iteration = 0; iteration < 10; ++iteration) {
        weightedSum(next.x, 1.0, current.x, a, pk);
        phi = next.fx = f(next.x, next.fxprime);
        phiPrime = dot(next.fxprime, pk);
        if ((phi > (phi0 + c1 * a * phiPrime0)) ||
            (iteration && (phi >= phi_old))) {
            return zoom(a0, a, phi_old);
        }
        if (Math.abs(phiPrime) <= -c2 * phiPrime0) {
            return a;
        }
        if (phiPrime >= 0) {
            return zoom(a, a0, phi);
        }
        phi_old = phi;
        a0 = a;
        a *= 2;
    }
    return a;
}