LineSearch.h

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#ifndef PBAT_MATH_OPTIMIZATION_LINESEARCH_H
#define PBAT_MATH_OPTIMIZATION_LINESEARCH_H
 
#include "pbat/Aliases.h"
 
#include <Eigen/Core>
 
namespace pbat::math::optimization {
 
template <class TScalar = Scalar>
struct BackTrackingLineSearch
{
    int nMaxIters{20}; 
    TScalar tau{0.5};  
    TScalar c{1e-4};   
    TScalar alpha{1};  
    BackTrackingLineSearch(
        int nMaxIters = 20,
        TScalar tau   = TScalar(0.5),
        TScalar c     = TScalar(1e-4),
        TScalar alpha = TScalar(1));
    template <class FObjective, class TDerivedG, class TDerivedDX, class TDerivedX>
    TScalar Solve(
        FObjective f,
        Eigen::MatrixBase<TDerivedG> const& g,
        Eigen::MatrixBase<TDerivedDX> const& dx,
        Eigen::MatrixBase<TDerivedX>& xk) const;
};
 
template <class TScalar>
inline BackTrackingLineSearch<TScalar>::BackTrackingLineSearch(
    int nMaxItersIn,
    TScalar tauIn,
    TScalar cIn,
    TScalar alphaIn)
    : nMaxIters(nMaxItersIn), tau(tauIn), c(cIn), alpha(alphaIn)
{
}
 
template <class TScalar>
template <class FObjective, class TDerivedG, class TDerivedDX, class TDerivedX>
inline TScalar BackTrackingLineSearch<TScalar>::Solve(
    FObjective f,
    Eigen::MatrixBase<TDerivedG> const& g,
    Eigen::MatrixBase<TDerivedDX> const& dx,
    Eigen::MatrixBase<TDerivedX>& xk) const
{
    TScalar alphaj    = alpha;
    TScalar const Dfk = g.dot(dx);
    TScalar fk        = f(xk);
    for (auto j = 0; j < nMaxIters; ++j)
    {
        TScalar flinear = fk + (c * alphaj) * Dfk;
        xk              = xk + alphaj * dx;
        fk              = f(xk);
        if (fk <= flinear)
            break;
        alphaj *= tau;
    }
    return alphaj;
}
 
} // namespace pbat::math::optimization
 
#endif // PBAT_MATH_OPTIMIZATION_LINESEARCH_H