3 citations · 5 across the 10 of their papers we have counts for
8 papers · 1 filter
Generalized gradient flows in Hadamard manifolds and convex optimization on entanglement polytopes
Hiroshi Hirai
In this paper, we address the optimization problem of minimizing over a Hadamard manifold , where is a convex function on , is the differen…
A scaling characterization of nc-rank via unbounded gradient flow
Hiroshi Hirai
Given a tuple of complex matrices , the linear symbolic matrix is nonsingular in the noncomm…
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 on a Hadamard manifold , particularly…
Interior-point methods on manifolds: theory and applications
Hiroshi Hirai, Harold Nieuwboer, Michael Walter
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordan…
Computing the nc-rank via discrete convex optimization on CAT(0) spaces
Masaki Hamada, Hiroshi Hirai
In this paper, we address the noncommutative rank (nc-rank) computation of a linear symbolic matrix \[ A = A_1 x_1 + A_2 x_2 + \cdots + A_m x_m, \] where each is an $n \times…
Computing the degree of determinants via discrete convex optimization on Euclidean buildings
Hiroshi Hirai
In this paper, we consider the computation of the degree of the Dieudonné determinant of a linear symbolic matrix , where each is an $n…