core/vnl/algo/vnl_lbfgs.h

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// This is core/vnl/algo/vnl_lbfgs.h
#ifndef vnl_lbfgs_h_
#define vnl_lbfgs_h_
#ifdef VCL_NEEDS_PRAGMA_INTERFACE
#pragma interface
#endif
//:
// \file
// \brief Limited memory Broyden Fletcher Goldfarb Shannon minimization
// \author Andrew W. Fitzgibbon, Oxford RRG
// \date   22 Aug 99
//
// \verbatim
// Modifications
//  990822 AWF Initial version.
//  dac (Manchester) 28/03/2001: tidied up documentation
//  scottim 4/02/2002: Added a better description
// \endverbatim
//

#include <vnl/vnl_cost_function.h>
#include <vnl/vnl_nonlinear_minimizer.h>

//: Limited memory Broyden Fletcher Goldfarb Shannon minimization
// Considered to be the best optimisation algorithm for functions
// which are well behaved (i.e. locally smooth
// without too many local minima,) have 1st derivatives available,
// and do not have a structure that makes them suitable for alternative
// methods (e.g. if f(x) is a sum of squared terms you should use
// vnl_levenberg_marquardt.)
//
// This limited-memory rank-2 quasi-newton method
// maintains an estimate of (the inverse of) the Hessian matrix of f at x.
// Unlike Newton's method, it doesn't need 2nd derivatives of f(x),
// has superlinear rather than quadratic convergence and is
// better behaved away from minima. 2 ranks of this matrix are updated at each
// step. In order to reduce memory and time requirements, this limited memory
// version of BFGS only maintains a certain number of vector corrections
// to a diagonal estimate of the inverse Hessian estimate.

class vnl_lbfgs : public vnl_nonlinear_minimizer
{
 public:
  vnl_lbfgs();
  vnl_lbfgs(vnl_cost_function& f);

  bool minimize(vnl_vector<double>& x);

  //: Step accuracy/speed tradeoff.
  // Effectively the number of correction vectors to the diagonal approximation
  // of the inverse Hessian estimate that are kept.
  //
  // Large values of M will result in excessive computing time.
  // 3<= memory <=7 is recommended.
  // Memory requirements will be roughly Const+sizeof(element)*dim(X)*memory.
  // Default is 5.
  int memory;

  //: Accuracy of line search.
  // If function evaluations are cheap wrt the actual minimization steps,
  // change to 0.1, from default of 0.9;
  double line_search_accuracy;

  //: Default step length in line search.
  // If, on tracing, the STP is always 1, then you could try setting this to a
  // higher value to see how far along the gradient the minimum typically is.
  // Then set this to a number just below that to get maximally far with the
  // single evaluation.
  double default_step_length;

 private:
  void init_parameters();
  vnl_cost_function* f_;
  //  vnl_lbfgs() {} // default constructor makes no sense
  // does too.  Can set values for parameters.
};

#endif // vnl_lbfgs_h_