Package net.finmath.optimizer
This package provides classes with numerical algorithm for optimization of an objective function and a factory to easy construction of the optimizers.
Why a package for optimization algorithms?
Given that there are a variety of numerical libraries featuring optimization algorithms
(e.g., Apache Commons Math), why do we provide a package inside finmath lib?
This packages provides a unified interface for passing optimizers to other classes
via an OptimizationFactoryInterface and an Optimizer
and an Optimizer.ObjectiveFunction.
This allows use of different optimization frameworks without bothering with the
framework specific constructors and framework specific definitions of objective functions.
A class implementing the OptimizationFactoryInterface allows the
specification of parameters specific to the optimizer, but leave the specification
of the initial values and the objective function still open. It provides a factory
method which takes the objective function and initial values as parameters and
constructs the specific optimizer by returning an object implementing
Optimizer.
The following code is an example of an optimization problem using an OptimizerFactory
as argument.
public void testOptimizerWithRosenbrockFunction(OptimizerFactory optimizerFactory) throws SolverException {
Optimizer.ObjectiveFunction objectiveFunction = new Optimizer.ObjectiveFunction() {
public void setValues(double[] parameters, double[] values) {
values[0] = 10.0 * (parameters[1] - parameters[0]*parameters[0]);
values[1] = 1.0 - parameters[0];
}
};
Optimizer optimizer = optimizerFactory.getOptimizer(
objectiveFunction,
new double[] { 0.5, 0.5 }, // initialParameters
new double[] { Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY }, // lowerBound
new double[] { Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY }, // upperBound
new double[] { 0.5, 0.5 }, // parameterStep
new double[] { 0.0, 0.0 }); // targetValues
optimizer.run();
double[] bestParameters = optimizer.getBestFitParameters();
System.out.println("The solver " + optimizer.getClass() + " for problem 'Rosebrock' required " + optimizer.getIterations() + " iterations. Accuracy is " + optimizer.getRootMeanSquaredError() + ". The best fit parameters are:");
for (int i = 0; i < bestParameters.length; i++) System.out.println("\tparameter[" + i + "]: " + bestParameters[i]);
System.out.println();
Assert.assertTrue(Math.abs(bestParameters[0] - 1.0) < 1E-10);
Assert.assertTrue(Math.abs(bestParameters[1] - 1.0) < 1E-10);
}
public void testRosenbrockFunctionWithCMAES() throws SolverException {
OptimizerFactory optimizerFactory = new OptimizerFactoryCMAES(0.0, 200);
this.testOptimizerWithRosenbrockFunction(optimizerFactory);
}
Or the multi-threadded Levenberg Marquardt solver (using two threads) from finmath-lib:
public void testRosenbrockFunctionWithLevenbergMarquard() throws SolverException {
OptimizerFactory optimizerFactory = new OptimizerFactoryLevenbergMarquardt(200, 2);
this.testOptimizerWithRosenbrockFunction(optimizerFactory);
}
Optimization algorithms
The package also contains an implementation of the Levenberg Marquardt optimizer,
a multi-dimensional non-linear least-square.
In addition we provide wrappers (via specific OptimizationFactoryInterface
implementations) to some optimizers from Apache commons-math.
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Interface SummaryInterfaceDescriptionInterface for numerical optimizers.Interface for the objective function.The interface describing the objective function of a
StochasticOptimizer. -
Class SummaryClassDescriptionThis class implements a Golden Section search algorithm, i.e., a minimization, implemented as a question-and-answer search algorithm.This class implements a parallel Levenberg-Marquardt non-linear least-squares fit algorithm.This class implements a stochastic Levenberg Marquardt non-linear least-squares fit algorithm.This class implements a stochastic Levenberg Marquardt non-linear least-squares fit algorithm.This class implements a stochastic Levenberg Marquardt non-linear least-squares fit algorithm.This class implements a stochastic Levenberg Marquardt non-linear least-squares fit algorithm.
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Enum SummaryEnumDescriptionThe regularization method used to invert the approximation of the Hessian matrix.The regularization method used to invert the approximation of the Hessian matrix.
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Exception Summary