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## Package org.apache.commons.math.optimization

This package provides common interfaces for the optimization algorithms provided in sub-packages.

See:
Description

Interface Summary
DifferentiableMultivariateRealOptimizer | This interface represents an optimization algorithm for `scalar differentiable objective functions`.
DifferentiableMultivariateVectorialOptimizer | This interface represents an optimization algorithm for `vectorial differentiable objective functions`.
MultivariateRealOptimizer | This interface represents an optimization algorithm for `scalar objective functions`.
RealConvergenceChecker | This interface specifies how to check if an `optimization algorithm` has converged.
UnivariateRealOptimizer | Interface for (univariate real) optimization algorithms.
VectorialConvergenceChecker | This interface specifies how to check if a `optimization algorithm` has converged.

Class Summary
LeastSquaresConverter | This class converts `vectorial objective functions` to `scalar objective functions` when the goal is to minimize them.
MultiStartDifferentiableMultivariateRealOptimizer | Special implementation of the `DifferentiableMultivariateRealOptimizer` interface adding multi-start features to an existing optimizer.
MultiStartDifferentiableMultivariateVectorialOptimizer | Special implementation of the `DifferentiableMultivariateVectorialOptimizer` interface adding multi-start features to an existing optimizer.
MultiStartMultivariateRealOptimizer | Special implementation of the `MultivariateRealOptimizer` interface adding multi-start features to an existing optimizer.
MultiStartUnivariateRealOptimizer | Special implementation of the `UnivariateRealOptimizer` interface adding multi-start features to an existing optimizer.
RealPointValuePair | This class holds a point and the value of an objective function at this point.
SimpleRealPointChecker | Simple implementation of the `RealConvergenceChecker` interface using only point coordinates.
SimpleScalarValueChecker | Simple implementation of the `RealConvergenceChecker` interface using only objective function values.
SimpleVectorialPointChecker | Simple implementation of the `VectorialConvergenceChecker` interface using only point coordinates.
SimpleVectorialValueChecker | Simple implementation of the `VectorialConvergenceChecker` interface using only objective function values.
VectorialPointValuePair | This class holds a point and the vectorial value of an objective function at this point.

Enum Summary
GoalType | Goal type for an optimization problem.

Exception Summary
OptimizationException | This class represents exceptions thrown by optimizers.

## Package org.apache.commons.math.optimization Description

This package provides common interfaces for the optimization algorithms provided in sub-packages. The main interfaces defines optimizers and convergence checkers. The functions that are optimized by the algorithms provided by this package and its sub-packages are a subset of the one defined in the `analysis` package, namely the real and vector valued functions. These functions are called objective function here. When the goal is to minimize, the functions are often called cost function, this name is not used in this package.

Optimizers are the algorithms that will either minimize or maximize, the objective function by changing its input variables set until an optimal set is found. There are only four interfaces defining the common behavior of optimizers, one for each supported type of objective function:

- `UnivariateRealOptimizer` for `univariate real functions`
- `MultivariateRealOptimizer` for `multivariate real functions`
- `DifferentiableMultivariateRealOptimizer` for `differentiable multivariate real functions`
- `DifferentiableMultivariateVectorialOptimizer` for `differentiable multivariate vectorial functions`

Despite there are only four types of supported optimizers, it is possible to optimize a transform a `non-differentiable multivariate vectorial function` by converting it to a `non-differentiable multivariate real function` thanks to the `LeastSquaresConverter` helper class. The transformed function can be optimized using any implementation of the `MultivariateRealOptimizer` interface.

For each of the four types of supported optimizers, there is a special implementation which wraps a classical optimizer in order to add it a multi-start feature. This feature call the underlying optimizer several times in sequence with different starting points and returns the best optimum found or all optima if desired. This is a classical way to prevent being trapped into a local extremum when looking for a global one.

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