Scatter search optimisation

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what optimisation algorithms are available.

Check those provided by SciPy's optimization and root finding library. All of them are available through the Sage interpreter by calling the appropriate scipy.optimize function. For example, the basin-hopping algorithm finds the global minimum of a scalar function:

sage: import numpy as np
sage: from scipy.optimize import basinhopping
sage: func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x
sage: x0=[1.]
sage: minimizer_kwargs = {"method": "BFGS"}
sage: ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs, niter=200)

                                              fun: -1.0008761844426548
          lowest_optimization_result:       fun: -1.0008761844426548
...

In some (but not all) cases, Sage provides an interface to these algorithms, so that you can directly use Sage symbolic functions as arguments.

It is worth mentioning that "out there" you'll find dozens of Python libraries for mathematical optimization (*). Notice that standard Python packages can be installed with the terminal command

$ sage --pip install --user package_name

and if the installation goes well, it is available the next time you start Sage via import package_name.

(*) See eg.:

• pymeigo, docs