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:

- {@link org.apache.commons.math.optimization.UnivariateRealOptimizer UnivariateRealOptimizer} for {@link org.apache.commons.math.analysis.UnivariateRealFunction univariate real functions}
- {@link org.apache.commons.math.optimization.MultivariateRealOptimizer MultivariateRealOptimizer} for {@link org.apache.commons.math.analysis.MultivariateRealFunction multivariate real functions}
- {@link org.apache.commons.math.optimization.DifferentiableMultivariateRealOptimizer DifferentiableMultivariateRealOptimizer} for {@link org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction differentiable multivariate real functions}
- {@link org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer DifferentiableMultivariateVectorialOptimizer} for {@link org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction differentiable multivariate vectorial functions}

Despite there are only four types of supported optimizers, it is possible to optimize a transform a {@link org.apache.commons.math.analysis.MultivariateVectorialFunction non-differentiable multivariate vectorial function} by converting it to a {@link org.apache.commons.math.analysis.MultivariateRealFunction non-differentiable multivariate real function} thanks to the {@link org.apache.commons.math.optimization.LeastSquaresConverter LeastSquaresConverter} helper class. The transformed function can be optimized using any implementation of the {@link org.apache.commons.math.optimization.MultivariateRealOptimizer 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.