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math.OC2026
Structured Preconditioning in Affine-Invariant Geometry: Projection, Certificates, and Kronecker Separation
Zavier Li
Nearest structured approximation and best structured preconditioning solve different matrix optimization problems. We determine their exact relation for Kronecker positive-definite…
math.OC2026
Restricted Dynamic Geometric Complexity: Path-Space Reduction and Möbius--Jacobi Response
Zavier Li
Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to…
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…