dev.nm.solver.multivariate.constrained.general.sqp.activeset

Class SQPASVariation1

java.lang.Object

dev.nm.solver.multivariate.constrained.general.sqp.activeset.SQPASVariation1

All Implemented Interfaces:

SQPASVariation

public class SQPASVariation1
extends Object
implements SQPASVariation

This implementation is a modified version of Algorithm 15.4 in the reference to solve a general constrained minimization problem using Sequential Quadratic Programming.

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Algorithm 15.4, SQP algorithm for nonlinear problems with equality and inequality constraints," Practical Optimization: Algorithms and Engineering Applications."

Constructor Summary

Constructors

Constructor and Description
SQPASVariation1(double epsilon) Construct a variation.

Method Summary

Modifier and Type	Method and Description
double	alpha(Vector x, Vector d, Vector v, Vector u) Get the percentage increment along the minimizer increment direction.
Matrix	getInitialHessian(Vector x0, Vector v0, Vector u0) Get the initial Hessian matrix.
void	set(RealScalarFunction f, RealVectorFunction g, EqualityConstraints equal, GreaterThanConstraints greater) Associate this variation to a particular general constrained minimization problem.
Matrix	updateHessian(Vector x1, Vector v1, Vector u1, Vector d, Vector g0, Matrix Ae0, Matrix Ai0, Matrix W0) Update the Hessian matrix using the latest iterates.

Methods inherited from class java.lang.Object

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

Constructor Detail

SQPASVariation1

public SQPASVariation1(double epsilon)

Construct a variation.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Method Detail

set

public void set(RealScalarFunction f,
                RealVectorFunction g,
                EqualityConstraints equal,
                GreaterThanConstraints greater)

Associate this variation to a particular general constrained minimization problem.

Parameters:

f - the objective function to be minimized

g - the gradient function for f

equal - the equality constraints

greater - the greater-than-or-equal-to constraints

getInitialHessian

public Matrix getInitialHessian(Vector x0,
                                Vector v0,
                                Vector u0)

Description copied from interface: SQPASVariation

Get the initial Hessian matrix.

Specified by:

getInitialHessian in interface SQPASVariation

Parameters:

x0 - the initial minimizer

v0 - the initial Lagrange multipliers for equality constraints (lambda)

u0 - the initial Lagrange multipliers for inequality constraints (mu)

Returns:

the initial Hessian matrix, e.g., identity

updateHessian

public Matrix updateHessian(Vector x1,
                            Vector v1,
                            Vector u1,
                            Vector d,
                            Vector g0,
                            Matrix Ae0,
                            Matrix Ai0,
                            Matrix W0)

Update the Hessian matrix using the latest iterates.

Specified by:

updateHessian in interface SQPASVariation

Parameters:

x1 - the next minimizer

v1 - the next Lagrange multipliers for equality constraints (lambda)

u1 - the next Lagrange multipliers for inequality constraints (mu)

d - the minimizer increment

g0 - the gradient

Ae0 - the set of active equality constraints

Ai0 - the set of active inequality constraints

W0 - the current Hessian matrix

Returns:

the next Hessian matrix

See Also:

"eqs. 15.41 - 15.44"

alpha

public double alpha(Vector x,
                    Vector d,
                    Vector v,
                    Vector u)

Get the percentage increment along the minimizer increment direction.

Specified by:

alpha in interface SQPASVariation

Parameters:

x - the current minimizer

d - the minimizer increment

v - the Lagrange multipliers for equality constraints (lambda)

u - the Lagrange multipliers for inequality constraints (mu)

Returns:

the percentage increment

See Also:

"eq. 15.36"