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directsearch
is a package for solving unconstrained minimization, without requiring derivatives of the objective. It is particularly useful when evaluations of the objective function are expensive and/or noisy.
It implements a family of direct search methods. For general references on these methods, please consult:
This package extends general direct search methods to use randomized methods for improved practical performance and scalability.
If you use this package, please cite:
L Roberts, and C W Royer. Direct search based on probabilistic descent in reduced spaces, In preparation, (2022).
Please install using pip:
.. code-block:: bash
$ pip install [--user] directsearch
To instead install from source run:
.. code-block:: bash
$ git clone git@github.com:lindonroberts/directsearch.git
$ cd directsearch
$ pip install -e .
The -e
option to pip allows you to modify the source code and for your Python installation to recognize this.
This package can solve unconstrained nonlinear optimization problems of the form: min_{x in R^n} f(x)
.
The simplest usage of directsearch
is
.. code-block:: python
soln = directsearch.solve(f, x0)
where
f
is a callable objective function, taking in a numpy.ndarray
the same shape as x0
and returing a single float
.x0
is a one-dimensional numpy.ndarray
(i.e. len(x0.shape)==1
), the starting point for the algorithm. It should be the best available guess of the minimizer.The output is an object with fields:
soln.x
: the approximate minimizer, the best x
value found (a numpy.ndarray
the same shape as x0
).soln.f
: the minimum value equal to f(soln.x)
.soln.nf
: the number of evaluations of f
required by the solve routine.soln.flag
: an integer indicating the reason for termination.soln.msg
: a string with a human-readable termination message.The possible values of soln.flag
are:
soln.EXIT_MAXFUN_REACHED
: termination on maximum number of objective evaluations.soln.EXIT_ALPHA_MIN_REACHED
: termination on small step size (success).You can print information about the solution using print(soln)
.
The examples
directory has several scripts showing the usage of directsearch
.
Interfaces to solver instances
There are many configurable options for the solver in directsearch
and several ways to call specific direct search algorithm implementations.
The full set of available functions is:
directsearch.solve()
applies a direct-search method to a given optimization problem. It is the most flexible available routine.directsearch.solve_directsearch()
applies regular direct-search techniques without sketching [1,2,3].directsearch.solve_probabilistic_directsearch()
applies direct search based on probabilistic descent without sketching [4].directsearch.solve_subspace_directsearch()
applies direct-search schemes based on polling directions in random subspaces [5].directsearch.solve_stp()
applies the stochastic three points method, a particular direct-search technique [6].Optional parameters and more information
See usage.txt
for full details on how to call these functions.
The most commonly used optional inputs (to all functions) are:
maxevals
: the maximum number of allowed evaluations of f
during the solve.verbose
: a bool
for whether or not to print progress information.print_freq
: an int
indicating how frequently to print progress information (1 is at every iteration).Choosing a solver instance
As a rule of thumb, if len(x0)
is not too large (e.g. less than 50), then solve_directsearch()
or solve_probabilistic_directsearch()
are suitable choices.
Of these, generally solve_probabilistic_directsearch()
will solve with fewer evaluations of f
, but solve_directsearch()
is a deterministic algorithm.
If len(x0)
is larger, then directsearch.solve_subspace_directsearch()
may be a better option.
Note that solve_directsearch()
is the only deterministic algorithm (i.e. reproducible without setting the numpy random seed).
References
Please report any bugs using GitHub's issue tracker.
This algorithm is released under the GNU GPL license.
FAQs
A derivative-free solver for unconstrained minimization
We found that directsearch demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
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