# SuanShu, a Java numerical and statistical library

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

## Class QPSimpleMinimizer

• java.lang.Object
• com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.socp.qp.QPSimpleMinimizer

• public class QPSimpleMinimizer
extends Object
These are the utility functions to solve simple quadratic programming problems that admit analytical solutions.
"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
QPSimpleMinimizer()
• ### Method Summary

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

• #### QPSimpleMinimizer

public QPSimpleMinimizer()
• ### Method Detail

• #### solve

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