com.joptimizer.functions

Class SDPLogarithmicBarrier

java.lang.Object

com.joptimizer.functions.SDPLogarithmicBarrier

All Implemented Interfaces:

BarrierFunction, TwiceDifferentiableMultivariateRealFunction

public class SDPLogarithmicBarrier
extends java.lang.Object
implements BarrierFunction

Generalized logarithmic barrier function for semidefinite programming.
If F(x) = G + Sum[x_i * F_i(x),i] is the constraint of the problem, then we have:
Φ = -logdet(-F(x))

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, p. 600"

Constructor Summary

Constructors

Constructor and Description
SDPLogarithmicBarrier(java.util.List<double[][]> FiMatrixList, double[][] GMatrix) Build the genaralized logarithmic barrier function for the constraint G + Sum[x_i * F_i(x),i] < 0, F_i, G symmetric matrices

Method Summary

Modifier and Type	Method and Description
double	calculatePhase1InitialFeasiblePoint(double[] originalNotFeasiblePoint, double tolerance) Calculates the initial value for the s parameter in Phase I.
BarrierFunction	createPhase1BarrierFunction() Create the barrier function for the Phase I.
int	getDim() Dimension of the function argument.
double	getDualityGap(double t) Calculates the duality gap for a barrier method build with this barrier function.
double[]	gradient(double[] X) Function gradient at point X.
double[][]	hessian(double[] X) Function hessian at point X.
double	value(double[] X) Evaluation of the function at point X.

Methods inherited from class java.lang.Object

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

Constructor Detail

SDPLogarithmicBarrier

public SDPLogarithmicBarrier(java.util.List<double[][]> FiMatrixList,
                             double[][] GMatrix)

Build the genaralized logarithmic barrier function for the constraint
G + Sum[x_i * F_i(x),i] < 0, F_i, G symmetric matrices

Parameters:

Fi - symmetric matrices

G - symmetric matrix

Method Detail

value

public double value(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Evaluation of the function at point X.

Specified by:

value in interface TwiceDifferentiableMultivariateRealFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, p. 618"

gradient

public double[] gradient(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Function gradient at point X.

Specified by:

gradient in interface TwiceDifferentiableMultivariateRealFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, p. 618"

hessian

public double[][] hessian(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Function hessian at point X.

Specified by:

hessian in interface TwiceDifferentiableMultivariateRealFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, p. 618"

createPhase1BarrierFunction

public BarrierFunction createPhase1BarrierFunction()

Create the barrier function for the Phase I. It is an instance of this class for the constraint:
G + Sum[x_i * F_i(x),i] < t * I

Specified by:

createPhase1BarrierFunction in interface BarrierFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.6.2"

calculatePhase1InitialFeasiblePoint

public double calculatePhase1InitialFeasiblePoint(double[] originalNotFeasiblePoint,
                                                  double tolerance)

Calculates the initial value for the s parameter in Phase I. Return s so that F(x)-s.I is negative definite

Specified by:

calculatePhase1InitialFeasiblePoint in interface BarrierFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.6.2", "S.Boyd and L.Vandenberghe, Semidefinite programming, 6.1"

getDim

public int getDim()

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Dimension of the function argument.

Specified by:

getDim in interface TwiceDifferentiableMultivariateRealFunction

getDualityGap

public double getDualityGap(double t)

Description copied from interface: BarrierFunction

Calculates the duality gap for a barrier method build with this barrier function.

Specified by:

getDualityGap in interface BarrierFunction