Line data    Source code

       1             : #pragma once
       2             : 
       3             : #include "LineSearchMethod.h"
       4             : 
       5             : namespace elsa
       6             : {
       7             :     /**
       8             :      * @brief Armijo Condition (Backtracking)
       9             :      *
      10             :      * ArmijoCondition is a line search method attempting to find a step size
      11             :      * @f$\alpha@f$ that satisfies the sufficient decrease condition (also known as the Armijo
      12             :      * Condition):
      13             :      *
      14             :      * @f[
      15             :      * f(x_i+\alpha d_i) \le f(x_i) + c \alpha \nabla f_i^T d_i
      16             :      * @f]
      17             :      *
      18             :      * where @f$f: \mathbb{R}^n \to \mathbb{R}@f$ is differentiable,
      19             :      * @f$\nabla f_i: \mathbb{R}^n is the gradient of f at x_i@f$,
      20             :      * @f$ d_i: \mathbb{R}^n is the search direction @f$, and
      21             :      * @f$ c: is a constant @f$.
      22             :      *
      23             :      * References:
      24             :      * - See Wright and Nocedal, ‘Numerical Optimization’, 2nd Edition, 2006, pp. 33-37.
      25             :      *
      26             :      * @author
      27             :      * - Said Alghabra - initial code
      28             :      *
      29             :      * @tparam data_t data type for the domain and range of the problem, defaulting to real_t
      30             :      */
      31             :     template <typename data_t = real_t>
      32             :     class ArmijoCondition : public LineSearchMethod<data_t>
      33             :     {
      34             :     public:
      35             :         ArmijoCondition(const Functional<data_t>& problem, data_t amax = 2, data_t c = 0.1,
      36             :                         data_t rho = 0.5, index_t max_iterations = 10);
      37           8 :         ~ArmijoCondition() override = default;
      38             : 
      39             :         /// make copy constructor deletion explicit
      40             :         ArmijoCondition(const ArmijoCondition<data_t>&) = delete;
      41             : 
      42             :         data_t solve(DataContainer<data_t> xi, DataContainer<data_t> di) override;
      43             : 
      44             :         /// implement the polymorphic comparison operation
      45             :         bool isEqual(const LineSearchMethod<data_t>& other) const override;
      46             : 
      47             :     private:
      48             :         // initial guess and largest allowed step size
      49             :         data_t _amax;
      50             : 
      51             :         // parameter affecting the sufficient decrease condition
      52             :         data_t _c;
      53             : 
      54             :         // reduction factor for the next step size guess
      55             :         data_t _rho;
      56             : 
      57             :         /// implement the polymorphic clone operation
      58             :         ArmijoCondition<data_t>* cloneImpl() const override;
      59             :     };
      60             : } // namespace elsa