com.numericalmethod.suanshu.optimization.constrained.convex.sdp.socp.qp

Class QPSimpleSolver

java.lang.Object

com.numericalmethod.suanshu.optimization.constrained.convex.sdp.socp.qp.QPSimpleSolver

public class QPSimpleSolver
extends java.lang.Object

These are the utility functions to solve simple quadratic programming problems that admit analytical solutions.

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Section 13.2, Convex QP Problems with Equality Constraints," Practical Optimization: Algorithms and Engineering Applications."

Constructor Summary

Constructors

Constructor and Description
QPSimpleSolver()

Method Summary

Modifier and Type	Method and Description
static QPSolution	solve(QuadraticFunction f) Solve an unconstrained quadratic programming problem of this form.
static QPSolution	solve(QuadraticFunction f, double epsilon) Solve an unconstrained quadratic programming problem of this form.
static QPSolution	solve(QuadraticFunction f, LinearEqualityConstraints equal) Solve a quadratic programming problem subject to equality constraints.
static QPSolution	solve(QuadraticFunction f, LinearEqualityConstraints equal, double epsilon) Solve a quadratic programming problem subject to equality constraints.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

QPSimpleSolver

public QPSimpleSolver()

Method Detail

solve

public static QPSolution solve(QuadraticFunction f,
                               double epsilon)
                        throws QPInfeasible

Solve an unconstrained quadratic programming problem of this form. \[ \min_x \left \{ \frac{1}{2} \times x'Hx + x'p \right \} \]

Parameters:

f - the objective function

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

a quadratic programming solution

Throws:

QPInfeasible - when the quadratic programming problem is infeasible

solve

public static QPSolution solve(QuadraticFunction f)
                        throws QPInfeasible

Solve an unconstrained quadratic programming problem of this form. \[ \min_x \left \{ \frac{1}{2} \times x'Hx + x'p \right \} \]

Parameters:

f - the objective function

Returns:

a quadratic programming solution

Throws:

QPInfeasible - when the quadratic programming problem is infeasible

solve

public static QPSolution solve(QuadraticFunction f,
                               LinearEqualityConstraints equal,
                               double epsilon)
                        throws QPInfeasible

Solve a quadratic programming problem subject to equality constraints. \[ \min_x \left \{ \frac{1}{2} \times x'Hx + x'p \right \}, Ax = b \]

Parameters:

f - the objective function

equal - the equality constraints

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

a quadratic programming solution

Throws:

QPInfeasible - when the quadratic programming problem is infeasible

solve

public static QPSolution solve(QuadraticFunction f,
                               LinearEqualityConstraints equal)
                        throws QPInfeasible

Solve a quadratic programming problem subject to equality constraints. \[ \min_x \left \{ \frac{1}{2} \times x'Hx + x'p \right \}, Ax = b \]

Parameters:

f - the objective function

equal - the equality constraints

Returns:

a quadratic programming solution

Throws:

QPInfeasible - when the quadratic programming problem is infeasible