public class QuadraticProgramming extends Object
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
subject to
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, , is used in the QP problem, then 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.
Modifier and Type | Class and Description |
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static class |
QuadraticProgramming.InconsistentSystemException
The system of constraints is inconsistent.
|
static class |
QuadraticProgramming.NoLPSolutionException
No solution for the LP problem with h = 0 was found by
DenseLP . |
static class |
QuadraticProgramming.ProblemUnboundedException
The object value for the problem is unbounded.
|
static class |
QuadraticProgramming.SolutionNotFoundException
A solution was not found.
|
Modifier and Type | Field and Description |
---|---|
static double |
EPSILON_SMALL
The smallest relative spacing for doubles.
|
Constructor and Description |
---|
QuadraticProgramming(double[][] h,
double[] g,
double[][] aEquality,
double[] bEquality,
double[][] aInequality,
double[] bInequality)
Solve a quadratic programming problem.
|
Modifier and Type | Method and Description |
---|---|
double[] |
getDual()
Returns the dual (Lagrange multipliers).
|
double |
getOptimalValue()
Returns the optimal value.
|
double[] |
getSolution()
Returns the solution.
|
boolean |
isNoMoreProgress()
Returns true if due to computer rounding error, a
change in the variables fail to improve the objective
function.
|
public static final double EPSILON_SMALL
public QuadraticProgramming(double[][] h, double[] g, double[][] aEquality, double[] bEquality, double[][] aInequality, double[] bInequality) throws QuadraticProgramming.InconsistentSystemException, QuadraticProgramming.ProblemUnboundedException, QuadraticProgramming.NoLPSolutionException, QuadraticProgramming.SolutionNotFoundException
h
- is square array containing the Hessian. It must be positive definite.g
- contains the coefficients of the linear term of the objective function.aEquality
- is a rectangular matrix containing the equality constraints.
It can be null if there are no equality constraints.bEquality
- contains the right-side of the equality constraints.
It can be null if there are no equality constraints.aInequality
- is a rectangular matrix containing the inequality constraints.
It can be null if there are no inequality constraints.bInequality
- contains the right-side of the inequality constraints.
It can be null if there are no inequality constraints.QuadraticProgramming.InconsistentSystemException
- if the system of constraints is
inconsistent and there is no solution.QuadraticProgramming.ProblemUnboundedException
QuadraticProgramming.NoLPSolutionException
QuadraticProgramming.SolutionNotFoundException
public double[] getDual()
public double getOptimalValue()
double
, the optimal value.public double[] getSolution()
public boolean isNoMoreProgress()
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Built October 13 2015.