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README.rst

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Minimal Function Cache
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~~~~~~~~~~~~~~~~~~~~~~
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``minimalFunctionCache`` is a optional package for ``cutgeneratingfunctiology`` which contains necessary data for using pre-computed cell descriptions of the space of continuous minimal functions with at most :math:`k` breakpoints where :math:`k=7`. This repository is in a beta state.
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Minimal Function Cache is a repository containing two packages python packages ``minimalFunctionCache`` and ``parametricCutGen``.
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This package is based on the dissertation of Acadia Larsen.
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``minimalFunctionCache`` is a optional package for ``cutgeneratingfunctiology`` which contains precomputed cell descptions of minimal functions with at most :math: `k` breakpoints where :math: `k=6`. This repository is in a beta state.
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Notes
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~~~~~
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``parametricCutGen`` is a package which implemments a single row optiomal cut selection for Mixed Integer Programs over the domain (and restricted domains) of continuous minimal functions with at most :math: `k` breakpoints. This repository is in an alpha state.
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- Data is written in .cvs files.
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- pip installable from cloned repository.
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- Tools to (re)generate data using a HPC.
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- Practical evidence for polyedral computational speed ups provided by ``pplite`` as compared to ``ppl``.
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These packages are based on the disseration of Acadia Larsen.
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Included Software and Tools
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~~~~~~~~~~~~~~~~~~~~~~~~~~~
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- ``minimalFunctionCache`` includes precomputed cell descriptions of minimal functions, code for generating the function cache on a HPC, and a comparison of ``ppl`` and ``pplite`` as polyhedral backends.
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- ``parametricCutGen`` is implemented to work with ``pyscipopt`` the python wrapper of ``SCIP``. This package includes a solver for cut selection problems over the domain (with possibly some constraints) of continuous minimal functions, an interface to ``pyscipopt`` and reproduceable parametric experinments for testing cut selection.
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Goals and Non-Goals
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~~~~~~~~~~~~~~~~~~~
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- Illustrate concept of explicit optimal cut selection as a proof of concept for MIP solvers.
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- Reproducibliblity of experimental data.
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- Mathematical correctness of cut generation up to some :math: `(M,\epsilon)` parameters.
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- Demonstrate use of ``passsagemath`` in application; in particular illustrate application of cutting edge mathematics to application of MIPs.
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Non-goals
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~~~~~~~~~
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- Performance and code optimization; the cut generation technique presented is a proof of concept and is intended to function (for practical problem) with an excess of compute.
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- Documenation; documentation and testing is minimal. What is written is what is requried to reproduce the results for an expert user.
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Documentation
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~~~~~~~~~~~~~
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Documentation is minimal as this repository is intended to be a purely optional data source for ``cutgeneratingfunctionology``.
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Installation
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~~~~~~~~~~~~
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- Start using the function cache in sagemath::
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cd ..
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sage
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sage: from cutgenerationfunctionology.igp import PiMinContConatiner
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sage: MinFun_with_at_most_5_breakpoints = PiMinContConatiner(5) # loaded with the function cache!
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sage: Pi5 = PiMinContConatiner(5) # loaded with the function cache!
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sage: Pi5_cell_description = [cell for cell in Pi5.get_semialgebraic_sets()]
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License
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~~~~~~~

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