3 papers
math.AG2025
Exposed extreme rays of the SONC cone
Mareike Dressler, Hongzhi Liao, Vera Roshchina
We provide a complete and explicit characterization of the exposed extreme rays of the cone of sums of nonnegative circuit (SONC) polynomials. The criterion we derive is purely com…
math.OC2024
Finite Convergence of Circumcentered-Reflection Method on Closed Polyhedral Cones in Euclidean Spaces
Hongzhi Liao
The Circumcentered Reflection Method (CRM) is a recently developed projection method for solving convex feasibility problems. It offers preferable convergence properties compared t…
math.OC2023
Douglas--Rachford is the best projection method
Minh N. Dao, Mareike Dressler, Hongzhi Liao +1
We prove that the Douglas--Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the…