Marc E. Pfetsch We propose a new subgradient method for the minimization of convex functions over a convex set. Common subgradient algorithms require an exact projection onto the feasible region in every iteration, which can be efficient only for problems that admit a fast projection. In our method we use inexact adaptive projections requiring to move within a … Read more
Given an undirected graph and a positive integer k, the maximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a non-trivial graph automorphism gives equivalent solutions. It is well known … Read more
Given an undirected node-weighted graph and a positive integer k, the maximum k-colorable subgraph probem is to select a k-colorable induced subgraph of largest weight. The natural integer programming formulation for this problem exhibits a high degree of symmetry which arises by permuting the color classes. It is well known that such symmetry has negative … Read more
The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up … Read more
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain … Read more