Class SteepestDescentMinimizer
- java.lang.Object
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- dev.nm.solver.multivariate.unconstrained.c2.steepestdescent.SteepestDescentMinimizer
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- All Implemented Interfaces:
Minimizer<C2OptimProblem,IterativeSolution<Vector>>,IterativeC2Minimizer,IterativeMinimizer<C2OptimProblem>,MultivariateMinimizer<C2OptimProblem,IterativeSolution<Vector>>,Optimizer<C2OptimProblem,IterativeSolution<Vector>>
- Direct Known Subclasses:
ConjugateGradientMinimizer,FirstOrderMinimizer,GaussNewtonMinimizer.MySteepestDescent,NewtonRaphsonMinimizer,PowellMinimizer,QuasiNewtonMinimizer,ZangwillMinimizer
public abstract class SteepestDescentMinimizer extends Object implements IterativeC2Minimizer
A steepest descent algorithm finds the minimum by moving along the negative of the steepest gradient direction. In each iteration, we compute a direction, e.g., dk = -g as in the first order approximation. We search along this direction for an improved minimizer by analytically computing αk that minimizes f(xk + αk * dk). The minimizer xk+1 = xk + αk * dk is updated. This procedure is repeated until the increment |αk * dk| becomes sufficiently small, hence convergence.- See Also:
- "Andreas Antoniou and Wu-Sheng Lu, "Algorithms 5.2, 5.3, 5.5," Practical Optimization: Algorithms and Engineering Applications."
- Wikipedia: Gradient descent
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Nested Class Summary
Nested Classes Modifier and Type Class Description protected classSteepestDescentMinimizer.SteepestDescentImplThis is an implementation of the steepest descent method.
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Field Summary
Fields Modifier and Type Field Description protected doubleepsilona precision parameter: when a number |x| ≤ ε, it is considered 0protected doublemaxIterationsthe maximum number of iterations
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Constructor Summary
Constructors Constructor Description SteepestDescentMinimizer(double epsilon, int maxIterations)Construct a multivariate minimizer using a steepest descent method.SteepestDescentMinimizer(LineSearch linesearch, double epsilon, int maxIterations)Construct a multivariate minimizer using a steepest descent method.
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description abstract IterativeSolution<Vector>solve(C2OptimProblem problem)Solve a minimization problem with a C2 objective function.
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Constructor Detail
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SteepestDescentMinimizer
public SteepestDescentMinimizer(LineSearch linesearch, double epsilon, int maxIterations)
Construct a multivariate minimizer using a steepest descent method.- Parameters:
linesearch- the line search method used in each iterationepsilon- a precision parameter: when a number |x| ≤ ε, it is considered 0maxIterations- the maximum number of iterations
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SteepestDescentMinimizer
public SteepestDescentMinimizer(double epsilon, int maxIterations)Construct a multivariate minimizer using a steepest descent method.- Parameters:
epsilon- a precision parameter: when a number |x| ≤ ε, it is considered 0maxIterations- the maximum number of iterations
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Method Detail
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solve
public abstract IterativeSolution<Vector> solve(C2OptimProblem problem) throws Exception
Solve a minimization problem with a C2 objective function.- Specified by:
solvein interfaceOptimizer<C2OptimProblem,IterativeSolution<Vector>>- Parameters:
problem- a minimization problem with a C2 objective function- Returns:
- a minimizer
- Throws:
Exception- when there is an error solving the problem
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