Interface for solving large-scale unconstrained optimization problems using L-BFGS. More...

Inheritance diagram for drwnOptimizer:

Public Member Functions
	drwnOptimizer ()
	default constructor

	drwnOptimizer (unsigned n)
	construct a problem with dimension n

	drwnOptimizer (const drwnOptimizer &o)
	copy constructor

void	initialize (unsigned n, const double *x=NULL)
	initialize an optimization problem of size n possibly with feasible starting point x $\mathbb{R}^n$ (or zero)

void	initialize (const double *x=NULL)
	initialize an optimization problem at feasible starting point x in $\mathbb{R}^n$ (or zero)

double	solve (unsigned maxiter, bool bMonitor=false)
	Solve the optimization problem for up to maxiter iterations to precision set by EPSF, EPSG, and EPSX static variables. Calls monitor function after each iteration if bMonitor is true.

virtual double	objective (const double *x) const =0
	returns value of objective function at point x

virtual void	gradient (const double x, double df) const =0
	populates gradient of objective function at point x

virtual double	objectiveAndGradient (const double x, double df) const
	returns value of objective function and populates gradient df at point x

unsigned	size () const
	dimension of optimization problem

double	operator[] (unsigned i) const
	returns the i-th component of the current solution

double &	operator[] (unsigned i)
	returns a reference to the i-th component of the current solution

virtual void	monitor (unsigned iter, double objValue)
	callback for each iteration during optimization (if bMonitor is true)

Public Attributes
unsigned	_n
	dimension of optimization problem (i.e., $\mathbb{R}^n$ )

double *	_x
	current feasible solution in $\mathbb{R}^n$

double *	_df
	gradient at _x in $\mathbb{R}^n$

Static Public Attributes
static double	EPSF = 1.0e-6
	default tolerance on function convergence

static double	EPSG = 1.0e-3
	deafult tolerance on gradient convergence

static double	EPSX = 1.0e-6
	default tolerance on solution convergence

Detailed Description

Interface for solving large-scale unconstrained optimization problems using L-BFGS.

Implements optimization using L-BFGS code is based on an implementation by Jorge Nocedal:

J. Nocedal. Updating Quasi-Newton Matrices with Limited Storage (1980), Mathematics of Computation 35, pp. 773-782.
D.C. Liu and J. Nocedal. On the Limited Memory Method for Large Scale Optimization (1989), Mathematical Programming B, 45, 3, pp. 503-528.

The derived class must override functions objective and gradient. It should also implement the objectiveAndGradient function for efficiency, and may override the monitor function. The monitor function can assume that _x contains the current estimate for the solution. Other functions should use the input argument.

This class tries to minimize the objective function define by objective.

The following simple example optimizes the one-dimensional function $f(x) = (x - 2)(x - 4)$ .

class MyObjective : public drwnOptimizer
{
  MyObjective() : drwnOptimizer(1) { }
  ~MyObjective() { }
  double objective(const double *x) const {
    return (x[0] - 2.0) * (x[0] - 4.0);
  }
  void gradient(const double *x, double *df) const {
    df[0] = 2.0 * (x[0] - 3.0);
  }
};
int main()
{
  MyObjective objFunction;
  double f_star = objFunction.solve(1000);
  double x_star = objFunction[0];
  cout << "f(" << x_star << ") = " << f_star << endl;
  return 0;
}

The documentation for this class was generated from the following files:

drwnOptimizer.h
drwnOptimizer.cpp

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description