Accord.Math.Optimization Namespace

Contains classes for constrained and unconstrained optimization. Includes Conjugate Gradient (CG), Bounded and Unbounded Broyden–Fletcher–Goldfarb–Shanno (BFGS), gradient-free optimization methods such as Cobyla and the Goldfarb-Idnani solver for Quadratic Programming (QP) problems.

Classes

	Class	Description
	AugmentedLagrangian	Augmented Lagrangian method for constrained non-linear optimization.
	BaseGradientOptimizationMethod	Base class for gradient-based optimization methods.
	BaseLeastSquaresMethod	Base class for least-squares optimizers implementing the ILeastSquaresMethod interface.
	BaseOptimizationMethod	Base class for optimization methods.
	BinarySearch	Binary search root finding algorithm.
	BoundedBroydenFletcherGoldfarbShanno	Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method.
	BoundedBroydenFletcherGoldfarbShannoInnerStatus	Inner status of the BoundedBroydenFletcherGoldfarbShanno optimization algorithm. This class contains implementation details that can change at any time.
	BrentSearch	Brent's root finding and minimization algorithms.
	BroydenFletcherGoldfarbShanno	Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method.
	Cobyla	Constrained optimization by linear approximation.
	ConjugateGradient	Conjugate Gradient (CG) optimization method.
	ConstraintExtensions	Extension methods on the IConstraint interface.
	FanChenLinQuadraticOptimization	General Sequential Minimal Optimization algorithm for Quadratic Programming problems.
	GaussNewton	Gauss-Newton algorithm for solving Least-Squares problems.
	GoldfarbIdnani	Goldfarb-Idnani Quadratic Programming Solver.
	GradientDescent	Gradient Descent (GD) for unconstrained optimization.
	LevenbergMarquardt	Levenberg-Marquardt algorithm for solving Least-Squares problems.
	LinearConstraint	Constraint with only linear terms.
	LinearConstraintCollection	Linear Constraint Collection.
	LineSearchFailedException	Line Search Failed Exception.
	Munkres	Hungarian method for solving the assignment problem, also known as the Kuhn–Munkres algorithm or Munkres assignment algorithm.
	NelderMead	Nelder-Mead simplex algorithm with support for bound constraints for non-linear, gradient-free optimization.
	NonlinearConjugateGradient	Non-linear Conjugate Gradient (WARNING: This code can not be used for commercial purposes. It is MANDATORY to check the accompanying license file for this particular module AND the source code for more details before you use this code).
	NonlinearConstraint	Constraint with only linear terms.
	NonlinearObjectiveFunction	Quadratic objective function.
	OptimizationProgressEventArgs	Optimization progress event arguments.
	QuadraticConstraint	Constraint with only quadratic terms.
	QuadraticObjectiveFunction	Quadratic objective function.
	ResilientBackpropagation	Resilient Backpropagation method for unconstrained optimization.
	Subplex	Subplex
	TrustRegionNewtonMethod	Simplified Trust Region Newton Method (TRON) for non-linear optimization.

Interfaces

	Interface	Description
	IConstraint	Defines an interface for an optimization constraint.
	IFunctionOptimizationMethodTInput, TOutput	Common interface for function optimization methods.
	IGradientOptimizationMethod	Common interface for function optimization methods which depend on having both an objective function and a gradient function definition available.
	IGradientOptimizationMethodTInput, TOutput	Common interface for function optimization methods which depend on having both an objective function and a gradient function definition available.
	ILeastSquaresMethod	Common interface for Least Squares algorithms, i.e. algorithms that can be used to solve Least Squares optimization problems.
	IObjectiveFunction	Common interface for specifying objective functions.
	IOptimizationMethod	Common interface for function optimization methods.
	IOptimizationMethodTCode	Common interface for function optimization methods.
	IOptimizationMethodTInput, TOutput	Common interface for function optimization methods.
	IOptimizationMethodTInput, TOutput, TCode	Common interface for function optimization methods.

Delegates

	Delegate	Description
	LeastSquaresFunction	Least Squares function delegate.
	LeastSquaresGradientFunction	Gradient function delegate.

Enumerations

	Enumeration	Description
	AugmentedLagrangianStatus	Status codes for the AugmentedLagrangian optimization algorithm.
	BoundedBroydenFletcherGoldfarbShannoStatus	Status codes for the BoundedBroydenFletcherGoldfarbShanno function optimizer.
	BrentSearchStatus	Status codes for the BrentSearch.
	BroydenFletcherGoldfarbShannoStatus	Status codes for the BroydenFletcherGoldfarbShanno function optimizer.
	CobylaStatus	Cobyla exit codes.
	ConjugateGradientCode	Conjugate Gradient exit codes.
	ConjugateGradientMethod	Conjugate gradient direction update formula.
	ConstraintType	Constraint type.
	GoldfarbIdnaniStatus	Status codes for the GoldfarbIdnani constrained quadratic programming solver.
	LineSearch	Line search algorithms.
	NelderMeadStatus	NelderMead exit codes.

Remarks

This namespace contains different methods for solving both constrained and unconstrained optimization problems. For unconstrained optimization, methods available include Conjugate Gradient (CG), Bounded and Unbounded Broyden–Fletcher–Goldfarb–Shanno (BFGS), Resilient Backpropagation and a simplified implementation of the Trust Region Newton Method (TRON).

For constrained optimization problems, methods available include the Augmented Lagrangian method for general non-linear optimization, Cobyla for gradient-free non-linear optimization, and the Goldfarb-Idnani method for solving Quadratic Programming (QP) problems.

This namespace also contains optimizers specialized for least squares problems, such as Gauss Newton and the Levenberg-Marquart least squares solvers.

For univariate problems, standard search algorithms are also available, such as Brent and Binary search.

The namespace class diagram is shown below.

Reference

Accord.Math

Accord.Math.Differentiation

Accord.Math.Integration