LineSearchBacktracking.h

// Copyright (C) 2016-2026 Yixuan Qiu <yixuan.qiu@cos.name>
// Under MIT license
 
#ifndef LBFGSPP_LINE_SEARCH_BACKTRACKING_H
#define LBFGSPP_LINE_SEARCH_BACKTRACKING_H
 
#include <Eigen/Core>
#include <stdexcept>  // std::runtime_error
#include "Param.h"
 
namespace LBFGSpp {

template <typename Scalar>
class LineSearchBacktracking
{
private:
    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
 
public:
    template <typename Foo>
    static void LineSearch(Foo& f, const LBFGSParam<Scalar>& param,
                           const Vector& xp, const Vector& drt, const Scalar& step_max,
                           Scalar& step, Scalar& fx, Vector& grad, Scalar& dg, Vector& x)
    {
        // Decreasing and increasing factors
        const Scalar dec = 0.5;
        const Scalar inc = 2.1;
 
        // Check the value of step
        if (step <= Scalar(0))
            throw std::invalid_argument("'step' must be positive");
 
        // Save the function value at the current x
        const Scalar fx_init = fx;
        // Projection of gradient on the search direction
        const Scalar dg_init = grad.dot(drt);
        // Make sure d points to a descent direction
        if (dg_init > 0)
            throw std::logic_error("the moving direction increases the objective function value");
 
        const Scalar test_decr = param.ftol * dg_init;
        Scalar width;
 
        int iter;
        for (iter = 0; iter < param.max_linesearch; iter++)
        {
            // x_{k+1} = x_k + step * d_k
            x.noalias() = xp + step * drt;
            // Evaluate this candidate
            fx = f(x, grad);
 
            if (fx > fx_init + step * test_decr || (fx != fx))
            {
                width = dec;
            }
            else
            {
                dg = grad.dot(drt);
 
                // Armijo condition is met
                if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
                    break;
 
                if (dg < param.wolfe * dg_init)
                {
                    width = inc;
                }
                else
                {
                    // Regular Wolfe condition is met
                    if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE)
                        break;
 
                    if (dg > -param.wolfe * dg_init)
                    {
                        width = dec;
                    }
                    else
                    {
                        // Strong Wolfe condition is met
                        break;
                    }
                }
            }
 
            if (step < param.min_step)
                throw std::runtime_error("the line search step became smaller than the minimum value allowed");
 
            if (step > param.max_step)
                throw std::runtime_error("the line search step became larger than the maximum value allowed");
 
            step *= width;
        }
 
        if (iter >= param.max_linesearch)
            throw std::runtime_error("the line search routine reached the maximum number of iterations");
    }
};
 
}  // namespace LBFGSpp
 
#endif  // LBFGSPP_LINE_SEARCH_BACKTRACKING_H