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math.OC2026
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…
math.OC2025
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…
math.OC2025
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…