DenseLP Class

DenseLP Class

Solves a linear programming problem using an active set strategy.

Inheritance Hierarchy

SystemObject
Imsl.MathDenseLP

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

Syntax

C++

Copy

[SerializableAttribute]
public class DenseLP

<SerializableAttribute>
Public Class DenseLP

[SerializableAttribute]
public ref class DenseLP

[<SerializableAttribute>]
type DenseLP =  class end

The DenseLP type exposes the following members.

Constructors

	Name	Description
	DenseLP(MPSReader)	Constructor using an MPSReader object.
	DenseLP(Double, Double, Double)	Constructor variables of type double.

Top

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.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetSolution	Returns the solution x of the linear programming problem.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetConstraintType	Sets the types of general constraints in the matrix a.
	SetLowerBound	Sets the lower bound, on the variables.
	SetUpperBound	Sets the upper bound, on the variables.
	SetUpperLimit	Sets the upper limit of the constraints.
	Solve	Solves the problem using an active set strategy.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

Top

Properties

	Name	Description
	IterationCount	Returns the number of iterations used.
	ObjectiveValue	Returns the optimal value of the objective function.
	RefinementType	The type of refinement used, if any.

Top

Remarks

Class DenseLP uses an active set strategy to solve linear programming problems, i.e., problems of the form

$\mathop {\min }\limits_{x\; \in \;R^n } c^T x$

subject to

$b_l \le Ax \le b_u$

$\,\,x_l \le x \le x_u$

where c is the objective coefficient vector, A is the coefficient matrix, and the vectors , , , and are the lower and upper bounds on the constraints and the variables, respectively.

If the linear constraints are infeasible an solution to the constraints are used as a replacement for the stated constraints. An exception is thrown but a generalized solution is computed and available using methods GetSolution or GetDualSolution. Similar comments hold for any of the three additional conditions:

There are multiple solutions;
some constraints are discarded, or
cycling in the algorithm is identified.

Refer to the following paper for further information: Krogh, Fred, T. (2005), An Algorithm for Linear Programming, http://mathalacarte.com/fkrogh/pub/lp.pdf , Tujunga, CA.

Reference

Imsl.Math Namespace

Other Resources

Example 1

Example 2

Example 3