com.numericalmethod.suanshu.optimization.constrained.general.sqp.activeset

Class SQPActiveSetSolver

java.lang.Object

com.numericalmethod.suanshu.optimization.constrained.general.sqp.activeset.SQPActiveSetSolver

All Implemented Interfaces:

ConstrainedMinimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, Minimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, Optimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, java.io.Serializable

Direct Known Subclasses:

SQPActiveSetSolverForOnlyInequalityConstraint

public class SQPActiveSetSolver
extends java.lang.Object
implements ConstrainedMinimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>

Sequential quadratic programming (SQP) is an iterative method for nonlinear optimization. SQP methods are used on problems for which the objective function and the constraints are twice continuously differentiable. SQP methods solve a sequence of optimization subproblems, each which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to Newton's method for finding a point where the gradient of the objective vanishes. If the problem has only equality constraints, then the method is equivalent to applying Newton's method to the first-order optimality conditions, or Karush–Kuhn–Tucker conditions, of the problem. SQP methods are the state of the art in nonlinear programming methods. Schittkowski has shown that SQP can outperform every other tested method in terms of efficiency, accuracy, and percentage of successful solutions, over a large number of test problems. The general minimization problem takes this form. \[ \min_x f(x) \textrm{ s.t.,} \\ a_i(x) = 0, i = 1, 2, ..., p\\ c_j(x) \geq 0, j = 1, 2, ..., q \]

See Also:

• Wikipedia: Sequential quadratic programming
• Wikipedia: Active set
• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 15.4, SQP algorithm for nonlinear problems with equality and inequality constraints," Practical Optimization: Algorithms and Engineering Applications."

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	SQPActiveSetSolver.Solution This is the solution to a general minimization with only inequality constraints using the SQP Active Set algorithm.
static interface	SQPActiveSetSolver.VariationFactory This factory constructs a new instance of SQPASVariation for each SQP problem.

Field Summary

Fields

Modifier and Type	Field and Description
protected double	epsilon
protected int	maxIterations

Constructor Summary

Constructors

Constructor and Description
SQPActiveSetSolver(double epsilon, int maxIterations) Construct an SQP Active Set minimizer to solve general minimization problems with inequality constraints.
SQPActiveSetSolver(SQPActiveSetSolver.VariationFactory variant, double epsilon, int maxIterations) Construct an SQP Active Set minimizer to solve general minimization problems with inequality constraints.

Method Summary

Modifier and Type	Method and Description
SQPActiveSetSolver.Solution	solve(ConstrainedOptimProblem 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

Field Detail

epsilon

protected final double epsilon

maxIterations

protected final int maxIterations

Constructor Detail

SQPActiveSetSolver

public SQPActiveSetSolver(SQPActiveSetSolver.VariationFactory variant,
                          double epsilon,
                          int maxIterations)

Construct an SQP Active Set minimizer to solve general minimization problems with inequality constraints.

Parameters:

variant - a factory that constructs a new instance of SQPASVariation for each problem

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

maxIterations - the maximum number of iterations

SQPActiveSetSolver

public SQPActiveSetSolver(double epsilon,
                          int maxIterations)

Construct an SQP Active Set minimizer to solve general minimization problems with inequality constraints.

Parameters:

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

maxIterations - the maximum number of iterations

Method Detail

solve

public SQPActiveSetSolver.Solution solve(ConstrainedOptimProblem problem)
                                  throws java.lang.Exception

Description copied from interface: Optimizer

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

Specified by:

solve in interface Optimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

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