meshi.optimizers
Class WolfConditionLineSearch

java.lang.Object
  meshi.optimizers.LineSearch
      meshi.optimizers.WolfConditionLineSearch

public class WolfConditionLineSearch
extends LineSearch

This class implements a line search that satisfies the Wolf conditions according to the scheme in: Numerical Optimization by J. Nocendal & S. J. Wright, Springer 1999, pp 55-62. Being in position Xk, and having a descent search direction Pk, a step length (alpha) is sought, that leads to a new position Xk+1, so that Xk+1 = Xk + alpha*Pk, and stisfies the 2 Wolf conditons: 1) E(Xk+1) < E(Xk) + c1*alpha*grad(Xk)*Pk (sufficient decrease) 2) |grad(Xk+1)*Pk| < c2*|grad(Xk)*Pk| (curvature condition) The implementation follows the one in the above reference. In short, the variable alpha is iteratively enlarged, until it brackets (with the previous iteration value) an interval that contain some points with the Wolf conditions. The function Zoom is then called, that finds the exact alpha where the Wolf conditions hold. The initial choice of alpha (at the first iteration) is the popular min{1 , -2*(E(Xk-1) - E(Xk))/(grad(Xk)*Pk)}. Other choices are possible to code if this one leads to failure of the line search algorithm. This algorithm is safe guarded against infinite loop, by a condition on the maximal number of energy evaluations. See bellow what to do if this condition is violated. How to use this class: ---------------------- a) Instantiate this class with the desired parameters. b) In a position Xk: evaluate the energy gradients and coordinates to position Xk. c) Run 'findStepLength(Vec[n][2])' where the first column in Vec is the position Xk, and the second column is the direction Pk. This method returns the found step length. This method also changes the coordinates in class 'energy' to the coordinates in the new (minimized) position: Xk+1 = Xk + (step_length)*Pk. Also the gradients in the energy class are updated. d) Check for thrown exceptions to make sure that the step length is correct. Parameters (Good default values are given after the parameter name) ---------- c1,c2 - 1e-4,0.9 - The two paramters of the Wolf conditions. Must satisfy: 0

Field Summary

private double	alphaFinal
private double	alphaI
private double	alphaI1
private double	c1
private double	c2
private double[][]	coordinates
private double	e0
private double	eI
private double	eI1
private double	extendAlphaFactor
private int	firstRun
private double	grad0
private double	gradI
private double	gradI1
private int	i
private double	interSafeGuard
private double	interSafeGuardFactor
private double	maxNumEvaluations
private int	n
private double	newE
private int	numAlphaEvaluations
private double	oldE
private int	stop

Fields inherited from class meshi.optimizers.LineSearch

energy

Constructor Summary

WolfConditionLineSearch(TotalEnergy energy, double c1, double c2, double extendAlphaFactor, int maxNumEvaluations)

Method Summary

double	findStepLength(double[][] inputCoordinates)
void	Reset()
void	Reset(double resAlpha)
private void	Zoom(double[][] inputCoordinates, int inv)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

maxNumEvaluations

private double maxNumEvaluations

extendAlphaFactor

private double extendAlphaFactor

c1

private double c1

c2

private double c2

interSafeGuardFactor

private final double interSafeGuardFactor

See Also:

Constant Field Values

interSafeGuard

private double interSafeGuard

oldE

private double oldE

newE

private double newE

coordinates

private double[][] coordinates

firstRun

private int firstRun

alphaI

private double alphaI

alphaI1

private double alphaI1

alphaFinal

private double alphaFinal

n

private int n

e0

private double e0

eI

private double eI

eI1

private double eI1

grad0

private double grad0

gradI

private double gradI

gradI1

private double gradI1

numAlphaEvaluations

private int numAlphaEvaluations

stop

private int stop

i

private int i

Constructor Detail

WolfConditionLineSearch

public WolfConditionLineSearch(TotalEnergy energy,
                               double c1,
                               double c2,
                               double extendAlphaFactor,
                               int maxNumEvaluations)

Method Detail

Reset

public void Reset()

Reset

public void Reset(double resAlpha)

findStepLength

public double findStepLength(double[][] inputCoordinates)
                      throws LineSearchException

Specified by:

findStepLength in class LineSearch

Throws:

LineSearchException

Zoom

private void Zoom(double[][] inputCoordinates,
                  int inv)