dev.nm.solver.multivariate.unconstrained.c2.steepestdescent

Class FirstOrderMinimizer

java.lang.Object

dev.nm.solver.multivariate.unconstrained.c2.steepestdescent.SteepestDescentMinimizer

dev.nm.solver.multivariate.unconstrained.c2.steepestdescent.FirstOrderMinimizer

All Implemented Interfaces:

Minimizer<C2OptimProblem,IterativeSolution<Vector>>, IterativeC2Minimizer, IterativeMinimizer<C2OptimProblem>, MultivariateMinimizer<C2OptimProblem,IterativeSolution<Vector>>, Optimizer<C2OptimProblem,IterativeSolution<Vector>>

public class FirstOrderMinimizer
extends SteepestDescentMinimizer

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

Nested Class Summary

Nested Classes

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

Nested classes/interfaces inherited from class dev.nm.solver.multivariate.unconstrained.c2.steepestdescent.SteepestDescentMinimizer

SteepestDescentMinimizer.SteepestDescentImpl

Field Summary

Fields inherited from class dev.nm.solver.multivariate.unconstrained.c2.steepestdescent.SteepestDescentMinimizer

epsilon, maxIterations

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
IterativeSolution<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

FirstOrderMinimizer

public FirstOrderMinimizer(FirstOrderMinimizer.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

FirstOrderMinimizer

public FirstOrderMinimizer(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 IterativeSolution<Vector> solve(C2OptimProblem problem)
                                throws Exception

Description copied from class: SteepestDescentMinimizer

Solve a minimization problem with a C² objective function.

Specified by:

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

Specified by:

solve in class SteepestDescentMinimizer

Parameters:

problem - a minimization problem with a C² objective function

Returns:

a minimizer

Throws:

Exception - when there is an error solving the problem