Solves the convex quadratic programming problem subject to equality or inequality constraints.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
[SerializableAttribute]
public class QuadraticProgramming
Visual Basic (Declaration)
<SerializableAttribute> _
Public Class QuadraticProgramming
Visual C++
[SerializableAttribute]
public ref class QuadraticProgramming

Remarks

Class QuadraticProgramming is based on M.J.D. Powell's implementation of the Goldfarb and Idnani dual quadratic programming (QP) algorithm for convex QP problems subject to general linear equality/inequality constraints (Goldfarb and Idnani 1983); i.e., problems of the form

\mathop {\min }\limits_{x \in R^n } g^Tx + \frac{1}{2} x^THx

subject to

A_1 x = b_1

A_2 x \ge b_2

given the vectors b_1, b_2, and g, and the matrices H, A_1, and A_2. H is required to be positive definite. In this case, a unique x solves the problem or the constraints are inconsistent. If H is not positive definite, a positive definite perturbation of H is used in place of H. For more details, see Powell (1983, 1985).

If a perturbation of H, H + \alpha I, is used in the QP problem, then H + \alpha I also should be used in the definition of the Lagrange multipliers.

If the constraints are infeasible an exception is thrown. See Example 3 where the exception is caught and printed.

Inheritance Hierarchy

System..::.Object
Imsl.Math..::.QuadraticProgramming

See Also