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The pseudo-Boolean polytope and polynomial-size extended formulations for binary polynomial optimization
- Publication Year :
- 2023
-
Abstract
- With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing pseudo-Boolean functions. By representing the pseudo-Boolean polytope via a signed hypergraph, we obtain sufficient conditions under which this polytope has a polynomial-size extended formulation. Our new framework unifies and extends all prior results on the existence of polynomial-size extended formulations for the convex hull of the feasible region of binary polynomial optimization problems of degree at least three.
- Subjects :
- Mathematics - Optimization and Control
Computer Science - Discrete Mathematics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2309.08693
- Document Type :
- Working Paper