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| <body> |
| <p> |
| 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 <code>analysis</code> |
| 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. |
| </p> |
| |
| <p> |
| 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: |
| <ul> |
| <li>{@link org.apache.commons.math.optimization.UnivariateRealOptimizer |
| UnivariateRealOptimizer} for {@link org.apache.commons.math.analysis.UnivariateRealFunction |
| univariate real functions}</li> |
| <li>{@link org.apache.commons.math.optimization.MultivariateRealOptimizer |
| MultivariateRealOptimizer} for {@link org.apache.commons.math.analysis.MultivariateRealFunction |
| multivariate real functions}</li> |
| <li>{@link org.apache.commons.math.optimization.DifferentiableMultivariateRealOptimizer |
| DifferentiableMultivariateRealOptimizer} for {@link |
| org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction |
| differentiable multivariate real functions}</li> |
| <li>{@link org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer |
| DifferentiableMultivariateVectorialOptimizer} for {@link |
| org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction |
| differentiable multivariate vectorial functions}</li> |
| </ul> |
| </p> |
| |
| <p> |
| 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. |
| </p> |
| |
| <p> |
| 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. |
| </p> |
| </body> |
| </html> |
