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math.OC2026
Yau's Affine Normal Descent: Algorithmic Framework and Convergence Analysis
Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau
We propose Yau's Affine Normal Descent (YAND), a geometric framework for smooth unconstrained optimization in which search directions are defined by the equi-affine normal of level…
math.OC2026
Affine Normal Directions via Log-Determinant Geometry: Scalable Computation under Sparse Polynomial Structure
Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau
Affine normal directions provide intrinsic affine-invariant descent directions derived from the geometry of level sets. Their practical use, however, has long been hindered by the…
math.OC2025★ 1 cited
An Improved Yau-Yau Algorithm for High Dimensional Nonlinear Filtering Problems
Shing-Tung Yau, Yi-Shuai Niu
Nonlinear state estimation under noisy observations is rapidly intractable as system dimension increases. We introduce an improved Yau-Yau filtering framework that breaks the curse…