| Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | <html> |
| 2 | <!-- |
| 3 | Licensed to the Apache Software Foundation (ASF) under one or more |
| 4 | contributor license agreements. See the NOTICE file distributed with |
| 5 | this work for additional information regarding copyright ownership. |
| 6 | The ASF licenses this file to You under the Apache License, Version 2.0 |
| 7 | (the "License"); you may not use this file except in compliance with |
| 8 | the License. You may obtain a copy of the License at |
| 9 | |
| 10 | http://www.apache.org/licenses/LICENSE-2.0 |
| 11 | |
| 12 | Unless required by applicable law or agreed to in writing, software |
| 13 | distributed under the License is distributed on an "AS IS" BASIS, |
| 14 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 15 | See the License for the specific language governing permissions and |
| 16 | limitations under the License. |
| 17 | --> |
| 18 | <!-- $Revision: 758074 $ --> |
| 19 | <body> |
| 20 | <p> |
| 21 | This package provides common interfaces for the optimization algorithms |
| 22 | provided in sub-packages. The main interfaces defines optimizers and convergence |
| 23 | checkers. The functions that are optimized by the algorithms provided by this |
| 24 | package and its sub-packages are a subset of the one defined in the <code>analysis</code> |
| 25 | package, namely the real and vector valued functions. These functions are called |
| 26 | objective function here. When the goal is to minimize, the functions are often called |
| 27 | cost function, this name is not used in this package. |
| 28 | </p> |
| 29 | |
| 30 | <p> |
| 31 | Optimizers are the algorithms that will either minimize or maximize, the objective function |
| 32 | by changing its input variables set until an optimal set is found. There are only four |
| 33 | interfaces defining the common behavior of optimizers, one for each supported type of objective |
| 34 | function: |
| 35 | <ul> |
| 36 | <li>{@link org.apache.commons.math.optimization.UnivariateRealOptimizer |
| 37 | UnivariateRealOptimizer} for {@link org.apache.commons.math.analysis.UnivariateRealFunction |
| 38 | univariate real functions}</li> |
| 39 | <li>{@link org.apache.commons.math.optimization.MultivariateRealOptimizer |
| 40 | MultivariateRealOptimizer} for {@link org.apache.commons.math.analysis.MultivariateRealFunction |
| 41 | multivariate real functions}</li> |
| 42 | <li>{@link org.apache.commons.math.optimization.DifferentiableMultivariateRealOptimizer |
| 43 | DifferentiableMultivariateRealOptimizer} for {@link |
| 44 | org.apache.commons.math.analysis.DifferentiableMultivariateRealFunction |
| 45 | differentiable multivariate real functions}</li> |
| 46 | <li>{@link org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer |
| 47 | DifferentiableMultivariateVectorialOptimizer} for {@link |
| 48 | org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction |
| 49 | differentiable multivariate vectorial functions}</li> |
| 50 | </ul> |
| 51 | </p> |
| 52 | |
| 53 | <p> |
| 54 | Despite there are only four types of supported optimizers, it is possible to optimize a |
| 55 | transform a {@link org.apache.commons.math.analysis.MultivariateVectorialFunction |
| 56 | non-differentiable multivariate vectorial function} by converting it to a {@link |
| 57 | org.apache.commons.math.analysis.MultivariateRealFunction non-differentiable multivariate |
| 58 | real function} thanks to the {@link |
| 59 | org.apache.commons.math.optimization.LeastSquaresConverter LeastSquaresConverter} helper class. |
| 60 | The transformed function can be optimized using any implementation of the {@link |
| 61 | org.apache.commons.math.optimization.MultivariateRealOptimizer MultivariateRealOptimizer} interface. |
| 62 | </p> |
| 63 | |
| 64 | <p> |
| 65 | For each of the four types of supported optimizers, there is a special implementation which |
| 66 | wraps a classical optimizer in order to add it a multi-start feature. This feature call the |
| 67 | underlying optimizer several times in sequence with different starting points and returns |
| 68 | the best optimum found or all optima if desired. This is a classical way to prevent being |
| 69 | trapped into a local extremum when looking for a global one. |
| 70 | </p> |
| 71 | </body> |
| 72 | </html> |