affine-invariant geometry 2condition number 1Hadamard spaces 1Jacobi response 1kronecker product 1matrix projection 1metric path optimization 1Möbius effects 1preconditioners 1riemannian optimization 1structured preconditioning 1
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math.OC2026
Structured Preconditioning in Affine-Invariant Geometry: Projection, Certificates, and Kronecker Separation
Zavier Li
The paper analyzes the relationship between affine‑invariant projection and optimal Kronecker‑structured preconditioning for positive‑definite matrices, proving that the unique pro…
math.OC2026
Restricted Dynamic Geometric Complexity: Path-Space Reduction and Möbius--Jacobi Response
Zavier Li
The paper introduces a framework for measuring the geometric effort needed to adjust preconditioners by defining a path‑space value problem that seeks the shortest affine‑invariant…
math.OC2026
Optimization Geometrodynamics: Variational Reduction and Interaction Curvature
Zavier Li
Adaptive optimizers carry hidden states that change how visible gradients become parameter motion. We develop optimization geometrodynamics as a variational theory of this hidden g…