H. Hirai

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20242026

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math.OC2026

Gradient descent for unbounded convex functions on Hadamard manifolds and its applications to scaling problems

Hiroshi Hirai, Keiya Sakabe

In this paper, we study the asymptotic behavior of continuous- and discrete-time gradient flows of a ``lower-unbounded" convex function $f$ on a Hadamard manifold $M$ , particularly…

math.OC2026

Generalized gradient flows in Hadamard manifolds and convex optimization on entanglement polytopes

Hiroshi Hirai

In this paper, we address the optimization problem of minimizing $Q (d f_{x})$ over a Hadamard manifold $M$ , where $f$ is a convex function on $M$ , $d f_{x}$ is the differen…

math.OC2025

A scaling characterization of nc-rank via unbounded gradient flow

Hiroshi Hirai

Given a tuple of $n \times n$ complex matrices $A = (A_{1}, A_{2}, \dots, A_{m})$ , the linear symbolic matrix $A = A_{1} x_{1} + A_{2} x_{2} + \dots + A_{m} x_{m}$ is nonsingular in the noncomm…