com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent

Class FirstOrder

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.FirstOrder

All Implemented Interfaces:

Minimizer<C2OptimProblem,IterativeMinimizer<Vector>>, Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>, MultivariateMinimizer<IterativeMinimizer<Vector>>, java.io.Serializable

public class FirstOrder
extends SteepestDescent

This implements the steepest descent line search using the first order expansion of the Taylor's series. Specifically, we search along the negative gradient direction.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 5.2," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Gradient descent

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	FirstOrder.Method the methods available to do line search

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

SteepestDescent.SteepestDescentImpl

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

epsilon, maxIterations

Constructor Summary

Constructors

Constructor and Description
FirstOrder(double epsilon, int maxIterations) Construct a multivariate minimizer using the First-Order method.
FirstOrder(FirstOrder.Method method, double epsilon, int maxIterations) Construct a multivariate minimizer using the First-Order method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(C2OptimProblem problem) Solve a minimization problem with a C2 objective function.

Methods inherited from class java.lang.Object

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

Constructor Detail

FirstOrder

public FirstOrder(FirstOrder.Method method,
                  double epsilon,
                  int maxIterations)

Construct a multivariate minimizer using the First-Order method.

Parameters:

method - the method to do line search

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

maxIterations - the maximum number of iterations

FirstOrder

public FirstOrder(double epsilon,
                  int maxIterations)

Construct a multivariate minimizer using the First-Order method. This line search is using Fletcher's inexact line search method.

Parameters:

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

maxIterations - the maximum number of iterations

Method Detail

solve

public IterativeMinimizer<Vector> solve(C2OptimProblem problem)
                                 throws java.lang.Exception

Description copied from class: SteepestDescent

Solve a minimization problem with a C² objective function.

Specified by:

solve in interface Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>

Specified by:

solve in class SteepestDescent

Parameters:

problem - a minimization problem with a C² objective function

Returns:

a minimizer

Throws:

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