org.apache.commons.math3.optim (Apache Commons Math 3.3 API)

# Package org.apache.commons.math3.optim

Generally, optimizers are algorithms that will either `minimize` or `maximize` a scalar function, called the `objective function`.

See: Description

- Interface Summary
  Interface | Description
  --- | ---
  ConvergenceChecker<PAIR> | This interface specifies how to check if an optimization algorithm has converged.
  OptimizationData | Marker interface.
  OptimizationProblem<PAIR> | Common settings for all optimization problems.

- Class Summary
  Class | Description
  --- | ---
  AbstractConvergenceChecker<PAIR> | Base class for all convergence checker implementations.
  AbstractOptimizationProblem<PAIR> | Base class for implementing optimization problems.
  BaseMultiStartMultivariateOptimizer<PAIR> | Base class multi-start optimizer for a multivariate function.
  BaseMultivariateOptimizer<PAIR> | Base class for implementing optimizers for multivariate functions.
  BaseOptimizer<PAIR> | Base class for implementing optimizers.
  InitialGuess | Starting point (first guess) of the optimization procedure.
  MaxEval | Maximum number of evaluations of the function to be optimized.
  MaxIter | Maximum number of iterations performed by an (iterative) algorithm.
  PointValuePair | This class holds a point and the value of an objective function at that point.
  PointVectorValuePair | This class holds a point and the vectorial value of an objective function at that point.
  SimpleBounds | Simple optimization constraints: lower and upper bounds.
  SimplePointChecker<PAIR extends Pair<double[],? extends Object>> | Simple implementation of the `ConvergenceChecker` interface using only point coordinates.
  SimpleValueChecker | Simple implementation of the `ConvergenceChecker` interface using only objective function values.
  SimpleVectorValueChecker | Simple implementation of the `ConvergenceChecker` interface using only objective function values.

## Package org.apache.commons.math3.optim Description

Generally, optimizers are algorithms that will either `minimize` or `maximize` a scalar function, called the `objective function`.
For some scalar objective functions the gradient can be computed (analytically or numerically). Algorithms that use this knowledge are defined in the `org.apache.commons.math3.optim.nonlinear.scalar.gradient` package. The algorithms that do not need this additional information are located in the `org.apache.commons.math3.optim.nonlinear.scalar.noderiv` package.

Some problems are solved more efficiently by algorithms that, instead of an objective function, need access to a `model function`: such a model predicts a set of values which the algorithm tries to match with a set of given `target values`. Those algorithms are located in the `org.apache.commons.math3.optim.nonlinear.vector` package.
Algorithms that also require the `Jacobian matrix of the model` are located in the `org.apache.commons.math3.optim.nonlinear.vector.jacobian` package.
The `non-linear least-squares optimizers` are a specialization of the the latter, that minimize the distance (called cost or χ2) between model and observations.
For cases where the Jacobian cannot be provided, a utility class will `convert` a (vector) model into a (scalar) objective function.

This package provides common functionality for the optimization algorithms. Abstract classes (`BaseOptimizer` and `BaseMultivariateOptimizer`) contain boiler-plate code for storing `evaluations` and `iterations` counters and a user-defined `convergence checker`.

For each of the optimizer types, there is a special implementation that wraps an optimizer instance and provides a "multi-start" feature: it calls the underlying optimizer several times with different starting points and returns the best optimum found, or all optima if so desired. This could be useful to avoid being trapped in a local extremum.

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