user_guide:tutorials:optimization

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user_guide:optimization [2019/01/25 09:27] – ↷ Links adapted because of a move operation oroehriguser_guide:tutorials:optimization [2019/01/25 10:56] – ↷ Links adapted because of a move operation oroehrig
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 There are several other tutorials that cover similar topics: There are several other tutorials that cover similar topics:
-  * [[user_guide:ilp_and_hilbertbases|ILP and Hilbert Bases]] +  * [[user_guide:tutorials:ilp_and_hilbertbases|ILP and Hilbert Bases]] 
-  * [[user_guide:michaels_tutorial2|Gomory Cuts]] +  * [[user_guide:tutorials:michaels_tutorial2|Gomory Cuts]] 
-  * [[user_guide:michaels_tutorial|Branch and Bound]] +  * [[user_guide:tutorials:michaels_tutorial|Branch and Bound]] 
-  * [[user_guide:lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]]+  * [[user_guide:tutorials:lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]]
  
 This tutorial is targeted towards the optimization community, since, surprisingly, polymake does not seem to be well known in this community. In particular, the community still tends to use the quite old program ''porta'' to compute convex hulls or inequality descriptions. While ''porta'' still does a decent job here, ''polymake'' offers a much broader feature set. Polymake supports several convex hull algorithms which might be better suited depending on the data. Moreover it offers many visualization tools that can help to better //understand// a given polytope. We think that polymake has many advantages for discrete optimizers and hope that this tutorial will help to spread the usage of polymake. This tutorial is targeted towards the optimization community, since, surprisingly, polymake does not seem to be well known in this community. In particular, the community still tends to use the quite old program ''porta'' to compute convex hulls or inequality descriptions. While ''porta'' still does a decent job here, ''polymake'' offers a much broader feature set. Polymake supports several convex hull algorithms which might be better suited depending on the data. Moreover it offers many visualization tools that can help to better //understand// a given polytope. We think that polymake has many advantages for discrete optimizers and hope that this tutorial will help to spread the usage of polymake.
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 ===== Integral Polytopes and Total Unimodularity ===== ===== Integral Polytopes and Total Unimodularity =====
  
-As explained in the previous example, the integral points in a polytope are of particular interest in discrete optimization. These points are called //lattice points// in polymake and the corresponding convex hull //lattice polytope//. The handling of such polytopes is explained in more detail in the [[user_guide:lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]].+As explained in the previous example, the integral points in a polytope are of particular interest in discrete optimization. These points are called //lattice points// in polymake and the corresponding convex hull //lattice polytope//. The handling of such polytopes is explained in more detail in the [[user_guide:tutorials:lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]].
  
 Of particular interest for discrete optimization are properties of the orginal inequality system to define a lattice polytope, i.e., a polytope such that all of its vertices are integral (this can be tested by checking the property ''LATTICE''). One particularly interesting case occurs if the matrix defining the polytope is //totally unimodular// and the right hand side is integral. Of particular interest for discrete optimization are properties of the orginal inequality system to define a lattice polytope, i.e., a polytope such that all of its vertices are integral (this can be tested by checking the property ''LATTICE''). One particularly interesting case occurs if the matrix defining the polytope is //totally unimodular// and the right hand side is integral.
  • user_guide/tutorials/optimization.txt
  • Last modified: 2019/02/04 22:55
  • by 127.0.0.1