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

Class QPPrimalActiveSetSolver

java.lang.Object

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

All Implemented Interfaces:

ConstrainedMinimizer<QPProblem,IterativeMinimizer<QPSolution>>, Minimizer<QPProblem,IterativeMinimizer<QPSolution>>, Optimizer<QPProblem,IterativeMinimizer<QPSolution>>, java.io.Serializable

public class QPPrimalActiveSetSolver
extends java.lang.Object
implements ConstrainedMinimizer<QPProblem,IterativeMinimizer<QPSolution>>

This implementation solves a Quadratic Programming problem using the Primal Active Set algorithm. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. A bottleneck is that only one constraint can be added or removed from the working set per iteration.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 13.1, Quadratic and Convex Programming," Practical Optimization: Algorithms and Engineering Applications."
• "Jorge Nocedal, Stephen Wright, "Algorithm 16.3," Numerical Optimization."
• Wikipedia: Active set

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	QPPrimalActiveSetSolver.Solution This is the solution to a Quadratic Programming problem using the Primal Active Set algorithm.

Constructor Summary

Constructors

Constructor and Description
QPPrimalActiveSetSolver(double epsilon, int maxIterations) Construct a Primal Active Set minimizer to solve quadratic programming problems.

Method Summary

Modifier and Type	Method and Description
QPPrimalActiveSetSolver.Solution	solve(QPProblem problem) Solve an optimization problem, e.g., OptimProblem.

Methods inherited from class java.lang.Object

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

Constructor Detail

QPPrimalActiveSetSolver

public QPPrimalActiveSetSolver(double epsilon,
                               int maxIterations)

Construct a Primal Active Set minimizer to solve quadratic programming problems.

Parameters:

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

maxIterations - the maximum number of iterations, e.g., Integer.MAX_VALUE

Method Detail

solve

public QPPrimalActiveSetSolver.Solution solve(QPProblem problem)
                                       throws java.lang.Exception

Description copied from interface: Optimizer

Solve an optimization problem, e.g., OptimProblem.

Specified by:

solve in interface Optimizer<QPProblem,IterativeMinimizer<QPSolution>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

java.lang.Exception - when there is an error solving the problem