5 papers
Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters
Mahmut Levent Doğan, Keiya Sakabe, Michael Walter
Convex optimization on polytopes arises in many areas of science. When the polytope is given implicitly or has exponentially many vertices and facets, standard methods may not appl…
Nesterov's accelerated gradient for unbounded convex functions finds the minimum-norm point in the dual space
Keiya Sakabe
We study the behavior of first-order methods applied to a lower-unbounded convex function , i.e., . Such a setting has received little attention since the traj…
Strassen's support functionals coincide with the quantum functionals
Keiya Sakabe, Mahmut Levent Doğan, Michael Walter
Strassen's asymptotic spectrum offers a framework for analyzing the complexity of tensors. It has found applications in diverse areas, from computer science to additive combinatori…
Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions
Gilles Barthe, Minbo Gao, Jam Kabeer Ali Khan +7
We present sound and complete relational program logics for infinite-dimensional quantum and classical-quantum programs. The logics model assertions as self-adjoint unbounded linea…
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…