QuadraticProgramming Class

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

For a list of all members of this type, see QuadraticProgramming Members.

System.Object
Imsl.Math.QuadraticProgramming

public class QuadraticProgramming

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

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

$A_2 x \ge b_2$

given the vectors , , and g, and the matrices H, , and . 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.

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

QuadraticProgramming Class

Thread Safety

Remarks

Requirements

See Also