BoundedVariableLeastSquares Class

Solve a linear least-squares problem with bounds on the variables.

Inheritance Hierarchy

SystemObject
Imsl.MathBoundedVariableLeastSquares

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

Copy

[SerializableAttribute]
public class BoundedVariableLeastSquares

<SerializableAttribute>
Public Class BoundedVariableLeastSquares

[SerializableAttribute]
public ref class BoundedVariableLeastSquares

[<SerializableAttribute>]
type BoundedVariableLeastSquares =  class end

The BoundedVariableLeastSquares type exposes the following members.

Constructors

	Name	Description
	BoundedVariableLeastSquares	Construct a new BoundedVariableLeastSquares instance to solve Ax-b subject to bounds on the variables. Each upper bound must be greater than or equal to the corresponding lower bound.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetDualSolution	Returns the dual solution vector, w.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetSolution	Returns the solution to the problem.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Solve	Find the solution x to the problem for the current constraints.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	Iterations	The number of iterations used to find the solution.
	MaxIterations	The maximum number of iterations.
	ResidualNorm	The euclidean norm of the residual vector, $\\|Ax-b\\|^2$ .
	Tolerance	The internal tolerance used to determine the relative linear dependence of a column vector for a variable moved from its initial value.

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Remarks

BoundedVariableLeastSquares solves the least-squares problem

$\min_x \| Ax-b\|^2$

subject to the conditions

$\alpha_k \le x_k \le \beta_k$

for all k.

This algorithm is a generalization of NonNegativeLeastSquares, that solves the least-squares problem, Ax = b, subject to all $x_j \ge 0$ . NonNegativeLeastSquares is based on the subroutine NNLS which appeared in Lawson and Hanson (1974). The additional work on bounded variable least squares was published in a later reprint (Lawson and Hanson, 1995).

Reference

Imsl.Math Namespace

Other Resources

Example