A Riemannian projected proximal gradient method is proposed and used to solve the problem. Numerical experimental results on synthetic benchmarks and real-world networks show that our algorithm is effective and outperforms several state-of-art algorithms....
而在Riemannian manifold setting 下,我们需要保证每一步的update 始终会回到该manifold上,而原本的 iprox 算子也将推广为 Riemannian proximal operator,用 Exp 算子和 Exp−1 拉回算子来保证每一步update都被限制在 manifold上。 图片摘自原文 最终,作者们成功将 Euclidean space 中 H-APE 推广到了 Riemannian ...
Carmo, M.P.: Riemannian Geometry. Birkhäuser, London (1992) MATH Google Scholar Chen, S., Ma, S., Man-Cho So, A., Zhang, T.: Proximal gradient method for nonsmooth optimization over the Stiefel manifold. SIAM J. Optim. 30, 210–239 (2020) MathSciNet MATH Google Scholar Chen,...
where\(\mathcal {M}\)is a Riemannian manifold andfis a real-valued function on\(\mathcal {M}\), which can be non-smooth. If additional constraints other than the manifold constraint are involved, we can add infan indicator function of the feasible set of these additional constraints. Hen...
The Incredible PyTorch: a curated list of tutorials, papers, projects, communities and more relating to PyTorch. - GitHub - ritchieng/the-incredible-pytorch: The Incredible PyTorch: a curated list of tutorials, papers, projects, communities and more rel
Shadowing is a phenomenon discovered in the study of hyperbolic differentiable dynamics, especially, in the study of geodesic flows on negatively curved closed Riemannian manifolds by Anosov [3] and Axiom A diffeomorphisms by Bowen [8]. It is one of “hyperbolic” features of dynamical systems, ...
RIEMANNIAN manifoldsNONCONVEX programmingMATHEMATICAL optimizationMATHEMATICAL inequalitiesMANIFOLDS (Mathematics)In this paper, we present a new approach to the proximal point method in the Riemannian context. In particular, without requiring any restrictive assumptions about the sign of the sectional curvature...
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to optimize the primal and dual variables iteratively. In each...
Ferreira, O.P.: Proximal subgradient and a characterization of Lipschitz function on Riemannian manifolds. J. Math. Anal. Appl. 313 , 587–597 (2006) MathSciNet MATHO.P. Ferreira, Proximal subgradient and a characterization of Lipschitz function on Riemannian manifolds, Journal of Mathematical...