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Mathematica 4.2: A Technical ReviewNew and Enhanced Packages Global Optimization
- differential evolution (genetic programming)
- Nelder–Mead (nonlinear simplex algorithm)
- simulated annealing
- random search
This loads the package.
This minimizes a quadratic function over a polyhedron.
This is the corresponding exact minimization.
Below are four examples that demonstrate how NMinimize handles some problems better than previous versions of FindMinimum Example This defines a function with a lot of local minima.
Here is a plot of the function.
This function cannot be easily handled using FindMinimum. If we start FindMinimum away from the global minimum, it gets trapped by a local minimum.
However, NMinimize finds the global minimum, with similar starting points.
Constrained Minimization Example NMinimize can solve problems including constraints in the case .
Solve Example
NMinimize can solve this problem easily if given a constant objective function and the equations to be solved as constraints.
NonlinearFit Example In this example, we generate a data set with random perturbations.
We first use NonlinearFit to try to fit a model to this data set.
As we see below, NonlinearFit gets trapped by a local minimum.
We can get a more accurate model by creating a sum of squares by hand and using NMinimize to find the minimum with the DifferentialEvolution method.
This approach creates a much better fit.
Statistical Analysis ANOVA is a statistical test for heterogeneity of means by analysis of group variances. The Statistics`ANOVA` package extends This loads the package.
This creates a simple univariate data set.
This computes the ANOVA table for the above data.
Here is another example data set.
Here is a plot for visualizing the data.
Here is the ANOVA table for the data.
Combinatorics
This loads the package.
You can use the package to generate a variety of graphs that are of interest in graph theory. For example, GridGraph[,] constructs an grid graph, the product of paths on and vertices.
The girth of a graph is the length of its shortest cycle. A cage is the smallest possible regular graph that has a prescribed girth. Here, we plot several cage graphs of degree 4. ShowGraphArray permits the display of multiple graphs in one window.
Here are some cage graphs of degree 5.
FiniteGraphs produces a list of all the interesting, finite, parameterless graphs built into Combinatorica.
The new
For more advanced functions and greater customizability, you can also evaluate the package functions directly. For more details on using the package, see “ |
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