Extended Formulations for Column Constrained Orbitopes

In the literature, packing and partitioning orbitopes were discussed to handle symmetries that act on variable matrices in certain binary programs. In this paper, we extend this concept by restrictions on the number of 1-entries in each column. We develop extended formulations of the resulting polytopes and present numerical results that show their effect on … Read more

Packing, Partitioning, and Covering Symresacks

In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering inequalities. To handle symmetries as well as set packing, partitioning, or covering constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and … Read more

A Dynamic Inequality Generation Scheme for Polynomial Programming

Hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small size. In this paper, we propose a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs. When used iteratively, this scheme improves … Read more