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NonNegativeLeastSquares Class
Solves a linear least squares problem with nonnegativity constraints.
Inheritance Hierarchy
SystemObject
  Imsl.MathNonNegativeLeastSquares

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
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[SerializableAttribute]
public class NonNegativeLeastSquares

The NonNegativeLeastSquares type exposes the following members.

Constructors
  NameDescription
Public methodNonNegativeLeastSquares
Construct a new NonNegativeLeastSquares instance to solve Ax-b where x is a vector of n unknowns.
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Methods
  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetDualSolution
Returns the dual solution vector, w. If x_j=0 then w_j\le 0, otherwise w_j = 0.
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetSolution
Returns the solution to the problem, x.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodSetGuess
Sets the initial guess.
Public methodSolve
Finds the solution to the problem for the current constraints.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyDualTolerance
The dual tolerance controlling when the computation stops.
Public propertyIterations
The number of iterations used to find the solution.
Public propertyMaximumTime
The maximum time allowed for the solve step.
Public propertyMaxIterations
The maximum number of iterations.
Public propertyNormTolerance
The residual norm tolerance.
Public propertyRankTolerance
The tolerance used for the incoming column rank deficient check.
Public propertyResidualNorm
The euclidean norm of the residual vector, \|Ax-b\|^2 .
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Remarks

NonNegativeLeastSquares solves the problem

\min_x\|Ax-b\|^2
subject to the condition x\ge 0.

If a starting point x_0 is provided, those entries of x_0 that are \gt0 are first combined with a descent gradient component. The start point is the origin. When x_0 is not provided the algorithm uses only the gradient to verify that an optimum has been found. The algorithm completes using only the gradient components to reach an optimum. For more information, see Lawson and Hanson (1974).

See Also