Splitting schemes

We provide the following splitting schemes:

• Proximal point algorithm;
• Gradient descent algorithm;
• Forward backward splitting;
• Backward forward splitting;
• Relaxed Peaceman Rachford splitting;
• 3 operator splitting (coming soon).

The following is a template for the splitting schemes. Each splitting scheme is a functor. The functor contains the pointers to the operators, and unknown variable.

class SchemeInterface {
public:
  //update internal scheme parameters
  virtual void update_params(Params* params) = 0;
  //compute and apply coordinate update, return S_{index}
  virtual double operator() (int index) =0;
  //compute and store S_{index} in variable S_i
  virtual void operator() (int index, double& S_i) =0;
  //apply block of S stored in s to solution vector
  virtual void update(Vector& s, int range_start, int num_cords) = 0;
  //apply coordinate of S stored in s to solution vector
  virtual void update(double s, int idx ) = 0;
  //update rank worth of cache_vars based on num_threads
  virtual void update_cache_vars(int rank, int num_threads) = 0;
};

In general, each splitting scheme will be templated on one or more operators. Operator objective will be defined as the member variables.

Note

Inside the parenthesis operator, relaxation will be used. Operator related cached variables will also be updated.