Class NullSpaceProjection

java.lang.Object

org.ojalgo.optimisation.convex.NullSpaceProjection

class NullSpaceProjection
extends Object

Null-Space Projection for Convex Optimisation Problems with Equality Constraints.

This class provides methods to reduce a convex optimisation problem with equality constraints to an equivalent problem without equality constraints, and fewer variables, by projecting onto the null-space of the equality constraint matrix. It uses QR decomposition to find a basis for the null-space and constructs the reduced problem accordingly.

There is of course some overhead in performing the reduction and in mapping solutions back and forth between the full and reduced problems, so this approach is most beneficial when the number of equality constraints is significant compared to the number of variables. In addition, the reduced problem may be denser than the original, which can impact solver performance.

Field Summary

Fields

Modifier and Type	Field	Description
private final QR<Double>	myDecomposition
private final ConvexData<Double>	myOriginal
private ConvexData<Double>	myReduced
private final MatrixStore<Double>	myX0
private final MatrixStore<Double>	myZ

Constructor Summary

Constructors

Constructor	Description
NullSpaceProjection(ConvexData<Double> original, QR<Double> decomposition, MatrixStore<Double> Z, MatrixStore<Double> x0)

Method Summary

Modifier and Type	Method	Description
(package private) ConvexData<Double>	getReduced()	Constructs and returns the reduced convex optimisation problem without equality constraints.
(package private) static NullSpaceProjection	reduce(ConvexData<Double> fullModel)	Reduces the given convex optimisation problem by eliminating equality constraints using null-space projection.
(package private) Optimisation.Result	toFullModelState(Optimisation.Result reducedlState)	Maps a solution of the reduced problem back to a solution of the original full problem.
(package private) Optimisation.Result	toReducedState(Optimisation.Result fullModelState)	Maps a solution of the full problem to a solution of the reduced problem.

Methods inherited from class Object

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

Field Details

myOriginal

private final ConvexData<Double> myOriginal

myDecomposition

private final QR<Double> myDecomposition

myZ

private final MatrixStore<Double> myZ

myX0

private final MatrixStore<Double> myX0

myReduced

private transient ConvexData<Double> myReduced

Constructor Details

NullSpaceProjection

NullSpaceProjection(ConvexData<Double> original,
 QR<Double> decomposition,
 MatrixStore<Double> Z,
 MatrixStore<Double> x0)

Method Details

reduce

static NullSpaceProjection reduce(ConvexData<Double> fullModel)

Reduces the given convex optimisation problem by eliminating equality constraints using null-space projection.

getReduced

ConvexData<Double> getReduced()

Constructs and returns the reduced convex optimisation problem without equality constraints.

toFullModelState

Optimisation.Result toFullModelState(Optimisation.Result reducedlState)

Maps a solution of the reduced problem back to a solution of the original full problem.

toReducedState

Optimisation.Result toReducedState(Optimisation.Result fullModelState)

Maps a solution of the full problem to a solution of the reduced problem. If the full problem solution is null or infeasible, null is returned.