5 papers
Graded families of ideals and convex regions
Haoxi Hu
We study the interplay between graded families of ideals in -domains and their associated convex regions. These regions, called Newton-Okounkov regions, arise naturally…
Finding Maximum Determinant Principal Submatrices via Hadamard Bounds and Projection Methods
Hao Hu, Stefan Sremac, Hugo J. Woerdeman +1
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This…
Affine FR: an Effective Facial Reduction Algorithm for Semidefinite Relaxations of Combinatorial Problems
Hao Hu, Boshi Yang
We develop a new method called affine facial reduction (FR) for recovering Slater's condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) prob…
The Maximum Singularity Degree for Linear and Semidefinite Programming
Hao Hu
Facial reduction (FR) is an important tool in linear and semidefinite programming, providing both algorithmic and theoretical insights into these problems. The maximum length of an…
Norm of the Hilbert matrix operator between some spaces of analytic functions
Hao Hu, Shanli Ye
In this paper, we calculate the exact value of the norm of the Hilbert matrix operator from the logarithmically weighted Korenblum space into Kor…