Sums of Nonnegative Circuit Polynomials and Combinatorics in Polynomial Optimization

• Applicants: Professor Dr. Thorsten Theobald; Professor Dr. Timo de Wolff
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 539847176

The project concerns studying sums of nonnegative circuit polynomials (SONC) and their use for sparse polynomial optimization. These concepts regard key ideas in the rapidly growing interplay of combinatorics, convexity and and non-linear optimization. The goal is to develop new combinatorial methods for the construction of certificates of nonnegativity in sparse contexts and the interaction of the SONC cone with a variety of combinatorial concepts, including convex cones, matroids, and lattice points. Specific working directions concern exactness results, convex-algebraic questions, generalized combinatorial models for the optimization and nonnegativity of sparse polynomials as well as selected applications.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2458: Combinatorial Synergies