Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
2024
Online
report
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbert bases, under the action of a finitely generated group. We also extend notions of total dual integrality, Gomory-Chv\'{a}tal closure, and Carath\'{e}odory rank to integer points in arbitrary cones.
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Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
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Autor/in / Beteiligte Person: | De Loera, Jesús A. ; Marsters, Brittney ; Xu, Luze ; Zhang, Shixuan |
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Veröffentlichung: | 2024 |
Medientyp: | report |
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