A second order cone characterization for sums of nonnegative circuits
The second-order cone (SOC) is a class of simple convex cones and optimizing over them
can be done more efficiently than with semidefinite programming. It is interesting both in …
can be done more efficiently than with semidefinite programming. It is interesting both in …
SONC optimization and exact nonnegativity certificates via second-order cone programming
The second-order cone (SOC) is a class of simple convex cones and optimizing over them
can be done more efficiently than with semidefinite programming. It is interesting both in …
can be done more efficiently than with semidefinite programming. It is interesting both in …
The duality of SONC: Advances in circuit-based certificates
J Heuer, T de Wolff - arXiv preprint arXiv:2204.03918, 2022 - arxiv.org
The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative
polynomials/exponential sums, which has been studied extensively in recent years. In this …
polynomials/exponential sums, which has been studied extensively in recent years. In this …
Geometrical study of the cone of sums of squares plus sums of nonnegative circuits
M Dressler, S Kuhlmann, M Schick - arXiv preprint arXiv:2305.14848, 2023 - arxiv.org
In this article, we combine sums of squares (SOS) and sums of nonnegative circuit (SONC)
forms, two independent nonnegativity certificates for real homogeneous polynomials. We …
forms, two independent nonnegativity certificates for real homogeneous polynomials. We …
Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation
J Wang - SIAM Journal on Optimization, 2024 - SIAM
We study optimal simple second-order cone representations (a particular subclass of
second-order cone representations) for weighted geometric means, which turns out to be …
second-order cone representations) for weighted geometric means, which turns out to be …
Weighted Geometric Mean, Minimum Mediated Set, and Optimal Second-Order Cone Representation
J Wang - arXiv preprint arXiv:2206.05924, 2022 - arxiv.org
We study optimal second-order cone representations for weighted geometric means, which
turns out to be closely related to minimum mediated sets. Several lower bounds and upper …
turns out to be closely related to minimum mediated sets. Several lower bounds and upper …